Lake 1
Describe data
Опишем имеющиеся данные:| vars | n | mean | sd | median | trimmed | mad | min | max | range | skew | kurtosis | se | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| depth | 1 | 12 | 14.00 | 7.21 | 14.00 | 14.00 | 8.90 | 3.00 | 25.00 | 22.00 | 0.00 | -1.50 | 2.08 |
| Li | 2 | 12 | 20.89 | 16.73 | 15.46 | 20.06 | 16.60 | 3.46 | 46.67 | 43.21 | 0.31 | -1.72 | 4.83 |
| Be | 3 | 12 | 0.98 | 0.49 | 0.93 | 0.95 | 0.61 | 0.42 | 1.84 | 1.43 | 0.29 | -1.49 | 0.14 |
| P | 4 | 12 | 2002.33 | 843.09 | 1846.50 | 1919.80 | 851.01 | 1077.00 | 3753.00 | 2676.00 | 0.66 | -0.82 | 243.38 |
| Sc | 5 | 12 | 11.04 | 5.50 | 9.44 | 10.75 | 5.64 | 5.49 | 19.49 | 14.00 | 0.30 | -1.74 | 1.59 |
| Ti | 6 | 12 | 1959.38 | 1533.96 | 1571.55 | 1884.58 | 1692.17 | 382.70 | 4284.00 | 3901.30 | 0.29 | -1.74 | 442.82 |
| V | 7 | 12 | 88.44 | 58.44 | 80.58 | 86.99 | 73.41 | 23.95 | 167.50 | 143.55 | 0.12 | -1.96 | 16.87 |
| Cr | 8 | 12 | 87.10 | 51.31 | 92.14 | 82.39 | 55.98 | 25.57 | 195.80 | 170.23 | 0.49 | -0.80 | 14.81 |
| Mn | 9 | 12 | 882.51 | 317.03 | 774.25 | 840.59 | 191.55 | 555.20 | 1629.00 | 1073.80 | 1.02 | -0.07 | 91.52 |
| Co | 10 | 12 | 16.58 | 6.29 | 15.14 | 16.57 | 8.35 | 7.23 | 26.00 | 18.77 | 0.07 | -1.52 | 1.81 |
| Ni | 11 | 12 | 55.54 | 19.82 | 53.68 | 55.21 | 24.44 | 29.68 | 84.70 | 55.02 | 0.14 | -1.81 | 5.72 |
| Cu | 12 | 12 | 112.60 | 62.16 | 108.65 | 106.05 | 70.88 | 44.37 | 246.40 | 202.03 | 0.74 | -0.57 | 17.94 |
| Zn | 13 | 12 | 276.19 | 93.03 | 285.50 | 277.11 | 94.89 | 121.70 | 421.50 | 299.80 | -0.19 | -1.21 | 26.86 |
| Ga | 14 | 12 | 8.78 | 6.43 | 7.16 | 8.51 | 7.37 | 1.94 | 18.24 | 16.30 | 0.25 | -1.80 | 1.86 |
| As | 15 | 12 | 10.07 | 6.61 | 7.34 | 9.31 | 3.47 | 3.32 | 24.41 | 21.09 | 0.91 | -0.63 | 1.91 |
| Rb | 16 | 12 | 46.49 | 38.12 | 34.88 | 44.60 | 38.11 | 8.04 | 103.90 | 95.86 | 0.29 | -1.75 | 11.00 |
| Sr | 17 | 12 | 72.54 | 26.73 | 68.75 | 71.80 | 34.00 | 40.71 | 111.80 | 71.09 | 0.14 | -1.85 | 7.72 |
| Y | 18 | 12 | 12.96 | 4.87 | 12.30 | 12.79 | 6.10 | 7.37 | 20.25 | 12.88 | 0.21 | -1.79 | 1.41 |
| Zr | 19 | 12 | 55.92 | 41.28 | 46.07 | 54.47 | 46.36 | 12.15 | 114.10 | 101.95 | 0.21 | -1.87 | 11.92 |
| Nb | 20 | 12 | 4.46 | 3.42 | 3.54 | 4.29 | 3.77 | 0.90 | 9.75 | 8.84 | 0.29 | -1.73 | 0.99 |
| Mo | 21 | 12 | 1.83 | 0.58 | 1.78 | 1.83 | 0.50 | 0.82 | 2.80 | 1.97 | 0.24 | -0.86 | 0.17 |
| Ag | 22 | 12 | 0.58 | 0.24 | 0.52 | 0.54 | 0.14 | 0.32 | 1.25 | 0.93 | 1.72 | 2.47 | 0.07 |
| Cd | 23 | 12 | 0.89 | 0.22 | 0.85 | 0.89 | 0.23 | 0.51 | 1.22 | 0.71 | 0.03 | -1.19 | 0.06 |
| Sn | 24 | 12 | 3.45 | 0.91 | 3.47 | 3.41 | 0.42 | 1.79 | 5.57 | 3.78 | 0.50 | 0.46 | 0.26 |
| Sb | 25 | 12 | 1.80 | 0.61 | 1.68 | 1.80 | 0.52 | 0.71 | 2.92 | 2.21 | 0.15 | -0.86 | 0.18 |
| Cs | 26 | 12 | 2.06 | 1.65 | 1.52 | 1.98 | 1.63 | 0.35 | 4.52 | 4.17 | 0.27 | -1.82 | 0.48 |
| Ba | 27 | 12 | 282.14 | 152.88 | 225.25 | 275.20 | 146.11 | 114.10 | 519.60 | 405.50 | 0.30 | -1.76 | 44.13 |
| La | 28 | 12 | 23.96 | 9.06 | 21.91 | 23.67 | 11.23 | 13.66 | 37.10 | 23.44 | 0.21 | -1.81 | 2.62 |
| Ce | 29 | 12 | 41.20 | 14.95 | 37.91 | 40.71 | 18.55 | 24.07 | 63.16 | 39.09 | 0.22 | -1.78 | 4.32 |
| Pr | 30 | 12 | 5.91 | 2.14 | 5.44 | 5.82 | 2.62 | 3.55 | 9.22 | 5.67 | 0.25 | -1.75 | 0.62 |
| Nd | 31 | 12 | 22.57 | 7.86 | 21.02 | 22.30 | 9.54 | 13.77 | 34.07 | 20.29 | 0.21 | -1.80 | 2.27 |
| Sm | 32 | 12 | 4.33 | 1.45 | 4.05 | 4.29 | 1.64 | 2.60 | 6.48 | 3.89 | 0.22 | -1.77 | 0.42 |
| Eu | 33 | 12 | 0.90 | 0.31 | 0.83 | 0.88 | 0.36 | 0.58 | 1.38 | 0.80 | 0.30 | -1.69 | 0.09 |
| Gd | 34 | 12 | 3.48 | 1.19 | 3.29 | 3.43 | 1.49 | 2.13 | 5.30 | 3.17 | 0.20 | -1.80 | 0.34 |
| Tb | 35 | 12 | 0.46 | 0.16 | 0.42 | 0.45 | 0.17 | 0.28 | 0.71 | 0.44 | 0.33 | -1.63 | 0.05 |
| Dy | 36 | 12 | 2.69 | 0.96 | 2.56 | 2.65 | 1.19 | 1.54 | 4.14 | 2.60 | 0.19 | -1.76 | 0.28 |
| Ho | 37 | 12 | 0.52 | 0.19 | 0.49 | 0.51 | 0.24 | 0.31 | 0.80 | 0.49 | 0.19 | -1.83 | 0.06 |
| Er | 38 | 12 | 1.50 | 0.60 | 1.38 | 1.48 | 0.75 | 0.82 | 2.38 | 1.56 | 0.20 | -1.83 | 0.17 |
| Tm | 39 | 12 | 0.21 | 0.09 | 0.20 | 0.20 | 0.11 | 0.11 | 0.33 | 0.22 | 0.10 | -1.89 | 0.02 |
| Yb | 40 | 12 | 1.31 | 0.57 | 1.20 | 1.30 | 0.70 | 0.68 | 2.13 | 1.45 | 0.17 | -1.88 | 0.16 |
| Lu | 41 | 12 | 0.19 | 0.09 | 0.17 | 0.18 | 0.11 | 0.10 | 0.33 | 0.23 | 0.31 | -1.66 | 0.03 |
| Hf | 42 | 12 | 1.70 | 1.24 | 1.38 | 1.64 | 1.35 | 0.38 | 3.52 | 3.15 | 0.25 | -1.82 | 0.36 |
| Ta | 43 | 12 | 0.35 | 0.27 | 0.29 | 0.34 | 0.30 | 0.06 | 0.76 | 0.70 | 0.28 | -1.73 | 0.08 |
| W | 44 | 12 | 1.20 | 0.47 | 1.37 | 1.23 | 0.51 | 0.35 | 1.76 | 1.41 | -0.45 | -1.37 | 0.14 |
| Tl | 45 | 12 | 0.47 | 0.21 | 0.42 | 0.46 | 0.23 | 0.19 | 0.80 | 0.60 | 0.28 | -1.58 | 0.06 |
| Pb | 46 | 12 | 54.24 | 11.06 | 56.04 | 54.54 | 13.29 | 35.56 | 69.97 | 34.41 | -0.24 | -1.36 | 3.19 |
| Bi | 47 | 12 | 0.28 | 0.07 | 0.29 | 0.28 | 0.09 | 0.18 | 0.40 | 0.21 | 0.16 | -1.36 | 0.02 |
| Th | 48 | 12 | 6.23 | 3.98 | 5.19 | 6.06 | 4.48 | 2.01 | 12.09 | 10.08 | 0.24 | -1.83 | 1.15 |
| U | 49 | 12 | 2.43 | 1.30 | 2.24 | 2.44 | 1.89 | 0.84 | 3.92 | 3.08 | 0.03 | -2.02 | 0.37 |
Матрица корреляций.
depth Li Be P Sc Ti V Cr Mn Co Ni
depth 1.00 NA NA NA NA NA NA NA NA NA NA
Li -0.75 1.00 NA NA NA NA NA NA NA NA NA
Be -0.74 0.97 1.00 NA NA NA NA NA NA NA NA
P 0.63 -0.80 -0.72 1.00 NA NA NA NA NA NA NA
Sc -0.75 1.00 0.97 -0.81 1.00 NA NA NA NA NA NA
Ti -0.76 1.00 0.97 -0.82 1.00 1.00 NA NA NA NA NA
V -0.84 0.99 0.96 -0.82 0.99 0.99 1.00 NA NA NA NA
Cr -0.61 0.78 0.67 -0.60 0.79 0.78 0.76 1.00 NA NA NA
Mn -0.90 0.56 0.57 -0.59 0.57 0.59 0.68 0.36 1.00 NA NA
Co -0.77 0.91 0.94 -0.69 0.89 0.90 0.92 0.51 0.68 1.00 NA
Ni -0.84 0.98 0.96 -0.78 0.98 0.98 0.99 0.73 0.69 0.95 1.00
Cu -0.82 0.51 0.53 -0.60 0.53 0.53 0.63 0.33 0.93 0.56 0.61
Zn -0.61 0.22 0.19 -0.03 0.23 0.23 0.28 0.59 0.42 0.11 0.28
Ga -0.76 1.00 0.96 -0.81 1.00 1.00 0.99 0.81 0.58 0.89 0.98
As 0.21 -0.32 -0.36 0.52 -0.32 -0.32 -0.36 0.23 -0.43 -0.51 -0.35
Rb -0.76 1.00 0.97 -0.81 1.00 1.00 0.99 0.78 0.57 0.90 0.98
Sr -0.85 0.97 0.96 -0.76 0.97 0.97 0.99 0.67 0.72 0.96 0.99
Y -0.82 0.99 0.97 -0.79 0.99 0.99 1.00 0.76 0.64 0.92 1.00
Zr -0.78 0.99 0.96 -0.81 1.00 1.00 0.99 0.80 0.59 0.89 0.98
Nb -0.75 1.00 0.96 -0.80 1.00 1.00 0.98 0.81 0.56 0.89 0.98
Mo -0.73 0.61 0.58 -0.46 0.62 0.62 0.67 0.71 0.73 0.59 0.67
Ag -0.04 -0.19 -0.06 0.31 -0.20 -0.20 -0.15 -0.31 0.11 0.06 -0.11
Cd 0.28 -0.73 -0.63 0.83 -0.73 -0.73 -0.67 -0.60 -0.11 -0.48 -0.62
Sn -0.53 0.68 0.66 -0.36 0.68 0.67 0.66 0.83 0.36 0.56 0.66
Sb -0.29 -0.04 0.04 0.48 -0.04 -0.04 -0.01 0.20 0.19 0.02 0.05
Cs -0.74 1.00 0.96 -0.80 1.00 0.99 0.98 0.82 0.55 0.88 0.97
Ba -0.84 0.96 0.96 -0.80 0.96 0.97 0.98 0.64 0.70 0.96 0.99
La -0.79 1.00 0.97 -0.79 1.00 1.00 0.99 0.79 0.60 0.91 0.99
Ce -0.79 1.00 0.97 -0.79 1.00 1.00 0.99 0.79 0.60 0.91 0.99
Pr -0.79 1.00 0.96 -0.80 1.00 1.00 0.99 0.78 0.60 0.91 0.99
Nd -0.80 1.00 0.96 -0.80 1.00 1.00 0.99 0.79 0.61 0.91 0.99
Sm -0.79 1.00 0.97 -0.79 0.99 1.00 0.99 0.77 0.61 0.92 0.99
Eu -0.77 0.99 0.96 -0.81 0.99 1.00 0.99 0.75 0.60 0.91 0.98
Gd -0.82 0.99 0.96 -0.79 0.99 0.99 1.00 0.76 0.64 0.92 0.99
Tb -0.76 1.00 0.96 -0.80 0.99 1.00 0.98 0.77 0.58 0.91 0.98
Dy -0.81 0.99 0.96 -0.78 0.99 0.99 0.99 0.79 0.62 0.90 0.99
Ho -0.82 0.99 0.96 -0.80 0.99 0.99 1.00 0.77 0.64 0.92 0.99
Er -0.81 0.99 0.96 -0.81 0.99 1.00 0.99 0.77 0.64 0.92 0.99
Tm -0.83 0.98 0.96 -0.78 0.99 0.99 0.99 0.77 0.67 0.91 0.99
Yb -0.81 0.99 0.96 -0.81 0.99 1.00 1.00 0.77 0.64 0.92 0.99
Lu -0.78 0.99 0.97 -0.81 0.99 1.00 0.99 0.75 0.61 0.92 0.99
Hf -0.76 1.00 0.96 -0.81 1.00 1.00 0.99 0.82 0.57 0.88 0.98
Ta -0.76 1.00 0.96 -0.81 1.00 1.00 0.99 0.81 0.57 0.89 0.98
W -0.89 0.79 0.79 -0.53 0.80 0.80 0.84 0.78 0.75 0.76 0.85
Tl -0.73 0.99 0.96 -0.74 0.98 0.98 0.96 0.82 0.51 0.89 0.97
Pb -0.60 0.51 0.58 -0.14 0.51 0.50 0.54 0.52 0.53 0.56 0.56
Bi -0.56 0.81 0.81 -0.48 0.81 0.80 0.78 0.78 0.40 0.73 0.79
Th -0.74 0.99 0.94 -0.80 0.99 0.99 0.97 0.86 0.55 0.85 0.96
U -0.94 0.91 0.90 -0.78 0.91 0.92 0.97 0.69 0.84 0.90 0.96
Cu Zn Ga As Rb Sr Y Zr Nb Mo Ag
depth NA NA NA NA NA NA NA NA NA NA NA
Li NA NA NA NA NA NA NA NA NA NA NA
Be NA NA NA NA NA NA NA NA NA NA NA
P NA NA NA NA NA NA NA NA NA NA NA
Sc NA NA NA NA NA NA NA NA NA NA NA
Ti NA NA NA NA NA NA NA NA NA NA NA
V NA NA NA NA NA NA NA NA NA NA NA
Cr NA NA NA NA NA NA NA NA NA NA NA
Mn NA NA NA NA NA NA NA NA NA NA NA
Co NA NA NA NA NA NA NA NA NA NA NA
Ni NA NA NA NA NA NA NA NA NA NA NA
Cu 1.00 NA NA NA NA NA NA NA NA NA NA
Zn 0.35 1.00 NA NA NA NA NA NA NA NA NA
Ga 0.53 0.27 1.00 NA NA NA NA NA NA NA NA
As -0.49 0.61 -0.29 1.00 NA NA NA NA NA NA NA
Rb 0.53 0.22 1.00 -0.33 1.00 NA NA NA NA NA NA
Sr 0.65 0.26 0.96 -0.40 0.97 1.00 NA NA NA NA NA
Y 0.58 0.28 0.99 -0.33 0.99 0.99 1.00 NA NA NA NA
Zr 0.55 0.27 1.00 -0.30 1.00 0.97 0.99 1.00 NA NA NA
Nb 0.52 0.25 1.00 -0.29 1.00 0.96 0.99 1.00 1.00 NA NA
Mo 0.65 0.59 0.65 -0.04 0.61 0.65 0.64 0.64 0.63 1.00 NA
Ag 0.19 0.11 -0.20 -0.12 -0.20 -0.07 -0.16 -0.18 -0.21 0.11 1.00
Cd -0.18 0.14 -0.73 0.30 -0.74 -0.58 -0.67 -0.71 -0.74 -0.16 0.56
Sn 0.29 0.50 0.71 0.15 0.67 0.62 0.65 0.70 0.70 0.82 0.00
Sb 0.09 0.72 -0.02 0.57 -0.05 0.05 0.01 -0.02 -0.02 0.44 0.40
Cs 0.51 0.25 1.00 -0.28 1.00 0.95 0.98 1.00 1.00 0.65 -0.21
Ba 0.62 0.22 0.95 -0.43 0.97 0.99 0.98 0.96 0.96 0.58 -0.11
La 0.55 0.27 1.00 -0.30 1.00 0.98 1.00 1.00 1.00 0.65 -0.18
Ce 0.54 0.28 1.00 -0.29 1.00 0.98 1.00 1.00 1.00 0.64 -0.19
Pr 0.54 0.26 1.00 -0.31 1.00 0.98 1.00 0.99 1.00 0.63 -0.18
Nd 0.55 0.27 1.00 -0.30 1.00 0.98 1.00 1.00 1.00 0.64 -0.20
Sm 0.54 0.26 0.99 -0.31 1.00 0.98 1.00 1.00 0.99 0.63 -0.19
Eu 0.54 0.22 0.99 -0.34 1.00 0.97 0.99 0.99 0.99 0.59 -0.24
Gd 0.58 0.28 0.99 -0.33 0.99 0.99 1.00 0.99 0.99 0.64 -0.16
Tb 0.50 0.23 0.99 -0.31 1.00 0.97 0.99 0.99 0.99 0.61 -0.22
Dy 0.55 0.30 0.99 -0.27 0.99 0.98 1.00 0.99 0.99 0.65 -0.21
Ho 0.58 0.27 0.99 -0.33 0.99 0.98 1.00 0.99 0.99 0.64 -0.20
Er 0.58 0.27 0.99 -0.33 0.99 0.98 1.00 0.99 0.99 0.66 -0.19
Tm 0.61 0.30 0.99 -0.32 0.99 0.98 0.99 0.99 0.98 0.68 -0.16
Yb 0.59 0.27 0.99 -0.34 1.00 0.98 1.00 0.99 0.99 0.65 -0.16
Lu 0.56 0.24 0.99 -0.34 0.99 0.98 1.00 0.99 0.99 0.61 -0.17
Hf 0.52 0.27 1.00 -0.28 1.00 0.96 0.99 1.00 1.00 0.65 -0.21
Ta 0.52 0.26 1.00 -0.28 1.00 0.96 0.99 1.00 1.00 0.63 -0.22
W 0.68 0.68 0.81 -0.02 0.79 0.84 0.83 0.82 0.80 0.89 0.16
Tl 0.45 0.29 0.99 -0.21 0.98 0.94 0.98 0.98 0.99 0.65 -0.13
Pb 0.52 0.54 0.53 0.01 0.50 0.57 0.53 0.53 0.51 0.81 0.51
Bi 0.38 0.34 0.82 -0.09 0.80 0.77 0.78 0.81 0.82 0.78 0.16
Th 0.51 0.29 1.00 -0.23 0.99 0.94 0.98 0.99 0.99 0.67 -0.23
U 0.78 0.39 0.92 -0.38 0.92 0.97 0.95 0.93 0.91 0.72 -0.05
Cd Sn Sb Cs Ba La Ce Pr Nd Sm Eu Gd Tb
depth NA NA NA NA NA NA NA NA NA NA NA NA NA
Li NA NA NA NA NA NA NA NA NA NA NA NA NA
Be NA NA NA NA NA NA NA NA NA NA NA NA NA
P NA NA NA NA NA NA NA NA NA NA NA NA NA
Sc NA NA NA NA NA NA NA NA NA NA NA NA NA
Ti NA NA NA NA NA NA NA NA NA NA NA NA NA
V NA NA NA NA NA NA NA NA NA NA NA NA NA
Cr NA NA NA NA NA NA NA NA NA NA NA NA NA
Mn NA NA NA NA NA NA NA NA NA NA NA NA NA
Co NA NA NA NA NA NA NA NA NA NA NA NA NA
Ni NA NA NA NA NA NA NA NA NA NA NA NA NA
Cu NA NA NA NA NA NA NA NA NA NA NA NA NA
Zn NA NA NA NA NA NA NA NA NA NA NA NA NA
Ga NA NA NA NA NA NA NA NA NA NA NA NA NA
As NA NA NA NA NA NA NA NA NA NA NA NA NA
Rb NA NA NA NA NA NA NA NA NA NA NA NA NA
Sr NA NA NA NA NA NA NA NA NA NA NA NA NA
Y NA NA NA NA NA NA NA NA NA NA NA NA NA
Zr NA NA NA NA NA NA NA NA NA NA NA NA NA
Nb NA NA NA NA NA NA NA NA NA NA NA NA NA
Mo NA NA NA NA NA NA NA NA NA NA NA NA NA
Ag NA NA NA NA NA NA NA NA NA NA NA NA NA
Cd 1.00 NA NA NA NA NA NA NA NA NA NA NA NA
Sn -0.29 1.00 NA NA NA NA NA NA NA NA NA NA NA
Sb 0.59 0.44 1.00 NA NA NA NA NA NA NA NA NA NA
Cs -0.74 0.73 -0.03 1.00 NA NA NA NA NA NA NA NA NA
Ba -0.63 0.54 -0.04 0.94 1.00 NA NA NA NA NA NA NA NA
La -0.70 0.70 0.01 0.99 0.97 1.00 NA NA NA NA NA NA NA
Ce -0.70 0.69 0.01 0.99 0.97 1.00 1.00 NA NA NA NA NA NA
Pr -0.70 0.67 -0.01 0.99 0.97 1.00 1.00 1.00 NA NA NA NA NA
Nd -0.70 0.67 -0.01 0.99 0.97 1.00 1.00 1.00 1.00 NA NA NA NA
Sm -0.69 0.67 0.00 0.99 0.98 1.00 1.00 1.00 1.00 1.00 NA NA NA
Eu -0.73 0.64 -0.06 0.99 0.97 0.99 0.99 1.00 1.00 0.99 1.00 NA NA
Gd -0.67 0.66 0.01 0.98 0.98 1.00 1.00 1.00 1.00 1.00 0.99 1.00 NA
Tb -0.71 0.66 -0.03 0.99 0.97 0.99 1.00 1.00 1.00 1.00 0.99 0.99 1.00
Dy -0.68 0.68 0.03 0.99 0.97 1.00 1.00 1.00 1.00 1.00 0.99 1.00 1.00
Ho -0.69 0.66 0.00 0.99 0.98 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.99
Er -0.70 0.68 -0.01 0.99 0.97 1.00 1.00 1.00 1.00 0.99 1.00 1.00 0.99
Tm -0.64 0.71 0.05 0.98 0.97 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.98
Yb -0.68 0.67 0.00 0.99 0.98 1.00 1.00 1.00 1.00 1.00 0.99 1.00 0.99
Lu -0.71 0.63 -0.03 0.98 0.98 0.99 1.00 1.00 0.99 0.99 1.00 0.99 0.99
Hf -0.73 0.71 -0.02 1.00 0.95 1.00 0.99 0.99 0.99 0.99 0.99 0.99 0.99
Ta -0.73 0.69 -0.02 1.00 0.96 1.00 1.00 1.00 1.00 0.99 0.99 0.99 1.00
W -0.27 0.81 0.48 0.81 0.79 0.83 0.82 0.81 0.82 0.81 0.77 0.83 0.79
Tl -0.68 0.75 0.06 0.99 0.94 0.99 0.99 0.98 0.98 0.98 0.97 0.97 0.98
Pb 0.10 0.80 0.67 0.53 0.48 0.54 0.53 0.52 0.52 0.52 0.47 0.53 0.49
Bi -0.41 0.91 0.31 0.84 0.71 0.82 0.80 0.80 0.79 0.79 0.76 0.79 0.79
Th -0.74 0.75 0.00 1.00 0.92 0.99 0.99 0.98 0.99 0.98 0.98 0.98 0.98
U -0.51 0.61 0.10 0.90 0.95 0.93 0.93 0.93 0.94 0.94 0.93 0.95 0.91
Dy Ho Er Tm Yb Lu Hf Ta W Tl Pb Bi Th U
depth NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Li NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Be NA NA NA NA NA NA NA NA NA NA NA NA NA NA
P NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Sc NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Ti NA NA NA NA NA NA NA NA NA NA NA NA NA NA
V NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Cr NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Mn NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Co NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Ni NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Cu NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Zn NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Ga NA NA NA NA NA NA NA NA NA NA NA NA NA NA
As NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Rb NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Sr NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Y NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Zr NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Nb NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Mo NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Ag NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Cd NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Sn NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Sb NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Cs NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Ba NA NA NA NA NA NA NA NA NA NA NA NA NA NA
La NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Ce NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Pr NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Nd NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Sm NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Eu NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Gd NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Tb NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Dy 1.00 NA NA NA NA NA NA NA NA NA NA NA NA NA
Ho 1.00 1.00 NA NA NA NA NA NA NA NA NA NA NA NA
Er 0.99 1.00 1.00 NA NA NA NA NA NA NA NA NA NA NA
Tm 0.99 0.99 0.99 1.00 NA NA NA NA NA NA NA NA NA NA
Yb 1.00 1.00 1.00 0.99 1.00 NA NA NA NA NA NA NA NA NA
Lu 0.99 0.99 0.99 0.99 0.99 1.00 NA NA NA NA NA NA NA NA
Hf 0.99 0.99 0.99 0.98 0.99 0.99 1.00 NA NA NA NA NA NA NA
Ta 0.99 0.99 0.99 0.98 0.99 0.99 1.00 1.00 NA NA NA NA NA NA
W 0.83 0.82 0.82 0.85 0.83 0.80 0.81 0.80 1.00 NA NA NA NA NA
Tl 0.98 0.97 0.98 0.97 0.98 0.98 0.99 0.99 0.82 1.00 NA NA NA NA
Pb 0.52 0.52 0.53 0.58 0.54 0.50 0.53 0.51 0.85 0.58 1.00 NA NA NA
Bi 0.79 0.78 0.79 0.81 0.80 0.78 0.82 0.81 0.84 0.87 0.83 1.00 NA NA
Th 0.98 0.98 0.98 0.98 0.98 0.98 1.00 0.99 0.82 0.98 0.54 0.84 1.0 NA
U 0.94 0.95 0.95 0.96 0.95 0.93 0.91 0.91 0.88 0.88 0.60 0.70 0.9 1Показываем только больше 0,5
Scree plot
Сколько факторов выбрать?
Loading required namespace: GPArotationThe determinant of the smoothed correlation was zero.
This means the objective function is not defined for the null model either.
The Chi square is thus based upon observed correlations.In factor.scores, the correlation matrix is singular, an approximation is used
Factor analysis
Проведём анализ с 3 факторами.
The determinant of the smoothed correlation was zero.
This means the objective function is not defined for the null model either.
The Chi square is thus based upon observed correlations.In factor.scores, the correlation matrix is singular, an approximation is usedFactor Analysis using method = minres
Call: fa(r = lake1, nfactors = 3)
Warning: A Heywood case was detected.
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR2 MR3 h2 u2 com
depth -0.63 -0.29 -0.41 0.87 1.3e-01 2.2
Li 1.01 -0.03 -0.03 1.00 3.3e-03 1.0
Be 0.94 0.01 0.07 0.93 7.4e-02 1.0
P -0.84 0.37 -0.13 0.80 2.0e-01 1.4
Sc 1.01 -0.03 -0.03 1.00 3.1e-03 1.0
Ti 1.01 -0.03 -0.01 1.00 6.9e-04 1.0
V 0.96 0.00 0.11 1.00 1.2e-03 1.0
Cr 0.84 0.35 -0.40 0.89 1.1e-01 1.8
Mn 0.40 0.19 0.69 0.86 1.4e-01 1.8
Co 0.83 -0.03 0.30 0.89 1.1e-01 1.3
Ni 0.95 0.03 0.13 0.99 9.6e-03 1.0
Cu 0.36 0.12 0.69 0.77 2.3e-01 1.6
Zn 0.15 0.77 -0.04 0.65 3.5e-01 1.1
Ga 1.01 0.01 -0.04 1.00 -3.7e-05 1.0
As -0.25 0.62 -0.64 0.82 1.8e-01 2.3
Rb 1.01 -0.04 -0.02 1.00 1.2e-03 1.0
Sr 0.91 0.02 0.21 0.99 1.2e-02 1.1
Y 0.98 0.00 0.06 0.99 5.7e-03 1.0
Zr 1.00 0.01 -0.01 0.99 5.2e-03 1.0
Nb 1.01 -0.01 -0.05 1.00 3.3e-04 1.0
Mo 0.51 0.55 0.19 0.76 2.4e-01 2.2
Ag -0.37 0.38 0.45 0.38 6.2e-01 2.9
Cd -0.89 0.52 0.35 0.90 9.9e-02 2.0
Sn 0.66 0.55 -0.24 0.81 1.9e-01 2.2
Sb -0.19 0.95 0.03 0.88 1.2e-01 1.1
Cs 1.01 0.01 -0.07 1.00 3.3e-03 1.0
Ba 0.93 -0.08 0.20 0.98 2.4e-02 1.1
La 1.00 0.02 0.00 1.00 1.1e-03 1.0
Ce 1.00 0.01 0.00 1.00 2.1e-03 1.0
Pr 1.00 -0.01 0.01 1.00 3.5e-03 1.0
Nd 1.00 0.00 0.01 1.00 2.0e-03 1.0
Sm 0.99 0.00 0.02 0.99 6.4e-03 1.0
Eu 1.00 -0.07 0.01 0.99 6.7e-03 1.0
Gd 0.98 0.01 0.06 0.99 6.8e-03 1.0
Tb 1.01 -0.03 -0.03 0.99 8.1e-03 1.0
Dy 0.99 0.03 0.00 0.99 6.4e-03 1.0
Ho 0.98 -0.01 0.05 1.00 4.2e-03 1.0
Er 0.99 0.00 0.04 1.00 3.4e-03 1.0
Tm 0.96 0.05 0.08 0.99 8.9e-03 1.0
Yb 0.98 0.01 0.06 1.00 1.1e-03 1.0
Lu 0.99 -0.04 0.04 0.99 9.6e-03 1.0
Hf 1.01 0.01 -0.06 1.00 1.4e-03 1.0
Ta 1.01 -0.01 -0.05 1.00 -2.1e-04 1.0
W 0.68 0.55 0.18 1.00 -2.3e-03 2.1
Tl 1.00 0.08 -0.10 0.98 1.7e-02 1.0
Pb 0.34 0.72 0.23 0.84 1.6e-01 1.7
Bi 0.76 0.39 -0.10 0.80 2.0e-01 1.5
Th 1.01 0.05 -0.11 1.00 4.2e-03 1.0
U 0.83 0.10 0.33 0.98 1.8e-02 1.3
MR1 MR2 MR3
SS loadings 38.17 4.51 2.98
Proportion Var 0.78 0.09 0.06
Cumulative Var 0.78 0.87 0.93
Proportion Explained 0.84 0.10 0.07
Cumulative Proportion 0.84 0.93 1.00
With factor correlations of
MR1 MR2 MR3
MR1 1.00 0.17 0.26
MR2 0.17 1.00 0.09
MR3 0.26 0.09 1.00
Mean item complexity = 1.3
Test of the hypothesis that 3 factors are sufficient.
The degrees of freedom for the null model are 1176 and the objective function was 1569.18 with Chi Square of -9676.59
The degrees of freedom for the model are 1032 and the objective function was NaN
The root mean square of the residuals (RMSR) is 0.03
The df corrected root mean square of the residuals is 0.03
The harmonic number of observations is 12 with the empirical chi square 24.38 with prob < 1
The total number of observations was 12 with Likelihood Chi Square = NaN with prob < NaN
Tucker Lewis Index of factoring reliability = NaN
Fit based upon off diagonal values = 1Каждый объединяет хим элементы следующим образом:
Loadings:
MR1 MR2 MR3
depth -0.628 -0.286 -0.414
Li 1.010
Be 0.940
P -0.839 0.369 -0.134
Sc 1.010
Ti 1.007
V 0.963 0.114
Cr 0.840 0.347 -0.402
Mn 0.398 0.190 0.688
Co 0.828 0.296
Ni 0.947 0.130
Cu 0.356 0.124 0.688
Zn 0.148 0.771
Ga 1.009
As -0.246 0.621 -0.643
Rb 1.010
Sr 0.913 0.213
Y 0.978
Zr 1.000
Nb 1.014
Mo 0.508 0.551 0.192
Ag -0.371 0.384 0.451
Cd -0.891 0.518 0.352
Sn 0.657 0.551 -0.235
Sb -0.186 0.950
Cs 1.013
Ba 0.926 0.204
La 0.995
Ce 0.997
Pr 0.997
Nd 0.997
Sm 0.993
Eu 1.004
Gd 0.977
Tb 1.008
Dy 0.992
Ho 0.985
Er 0.986
Tm 0.962
Yb 0.981
Lu 0.990
Hf 1.011
Ta 1.014
W 0.679 0.548 0.183
Tl 0.996 -0.102
Pb 0.342 0.719 0.233
Bi 0.764 0.385 -0.101
Th 1.011 -0.105
U 0.831 0.103 0.326
MR1 MR2 MR3
SS loadings 37.659 4.307 2.613
Proportion Var 0.769 0.088 0.053
Cumulative Var 0.769 0.856 0.9101 фактор описывает данные на 76.9%
1+2 факторы описывают данные на 85.6%
1+2+3 факторы описывают данные на 91% 
3D репрезентация исходных наблюдений в новом пространстве факторов.
Lake 2
Decribe data
Опишем имеющиеся данные:| vars | n | mean | sd | median | trimmed | mad | min | max | range | skew | kurtosis | se | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| depth | 1 | 26 | 21.38 | 13.94 | 19.00 | 20.91 | 17.79 | 1.00 | 47.00 | 46.00 | 0.26 | -1.29 | 2.73 |
| Li | 2 | 26 | 9.85 | 10.25 | 6.99 | 8.63 | 9.02 | 0.34 | 33.87 | 33.53 | 0.97 | -0.16 | 2.01 |
| Be | 3 | 26 | 0.71 | 0.31 | 0.70 | 0.69 | 0.33 | 0.26 | 1.40 | 1.14 | 0.46 | -0.61 | 0.06 |
| P | 4 | 26 | 17324.46 | 11904.09 | 17645.00 | 16999.27 | 16101.04 | 1544.00 | 37830.00 | 36286.00 | 0.12 | -1.40 | 2334.58 |
| Sc | 5 | 26 | 7.48 | 4.06 | 6.90 | 7.14 | 3.50 | 2.71 | 17.59 | 14.88 | 0.86 | -0.37 | 0.80 |
| Ti | 6 | 26 | 1112.73 | 1037.99 | 836.00 | 990.86 | 893.71 | 113.70 | 3439.00 | 3325.30 | 0.97 | -0.18 | 203.57 |
| V | 7 | 26 | 725.96 | 1219.21 | 122.11 | 459.30 | 154.15 | 16.97 | 4785.00 | 4768.03 | 2.10 | 3.72 | 239.11 |
| Cr | 8 | 26 | 47.83 | 40.17 | 35.63 | 41.69 | 25.17 | 10.14 | 179.30 | 169.16 | 1.62 | 2.36 | 7.88 |
| Mn | 9 | 26 | 2194.78 | 1218.19 | 2058.00 | 2146.50 | 1507.80 | 482.80 | 4400.00 | 3917.20 | 0.36 | -1.12 | 238.91 |
| Co | 10 | 26 | 17.20 | 3.87 | 17.34 | 17.21 | 3.23 | 9.52 | 25.18 | 15.66 | 0.13 | -0.28 | 0.76 |
| Ni | 11 | 26 | 145.85 | 176.47 | 53.64 | 116.46 | 45.25 | 9.67 | 606.50 | 596.83 | 1.47 | 0.97 | 34.61 |
| Cu | 12 | 26 | 381.89 | 344.39 | 263.45 | 342.25 | 270.52 | 39.81 | 1260.00 | 1220.19 | 0.96 | -0.18 | 67.54 |
| Zn | 13 | 26 | 456.35 | 166.92 | 455.80 | 447.87 | 124.61 | 136.00 | 962.60 | 826.60 | 0.75 | 1.30 | 32.74 |
| Rb | 14 | 26 | 25.28 | 26.51 | 17.41 | 21.43 | 20.96 | 1.35 | 91.64 | 90.29 | 1.22 | 0.55 | 5.20 |
| Sr | 15 | 26 | 71.59 | 21.19 | 70.20 | 70.78 | 13.29 | 26.31 | 118.80 | 92.49 | 0.42 | 0.12 | 4.16 |
| Y | 16 | 26 | 8.41 | 2.49 | 7.99 | 8.25 | 1.81 | 4.41 | 13.99 | 9.58 | 0.60 | -0.25 | 0.49 |
| Zr | 17 | 26 | 44.07 | 28.56 | 42.00 | 42.50 | 28.24 | 6.36 | 100.40 | 94.04 | 0.59 | -0.90 | 5.60 |
| Nb | 18 | 26 | 2.22 | 2.06 | 1.88 | 1.96 | 2.03 | 0.23 | 7.09 | 6.86 | 1.00 | 0.03 | 0.40 |
| Mo | 19 | 26 | 4.48 | 2.20 | 4.05 | 4.15 | 1.17 | 2.49 | 13.32 | 10.83 | 2.45 | 7.18 | 0.43 |
| Ag | 20 | 26 | 0.66 | 0.33 | 0.63 | 0.64 | 0.35 | 0.22 | 1.68 | 1.47 | 0.89 | 1.21 | 0.06 |
| Cd | 21 | 26 | 0.67 | 0.23 | 0.68 | 0.67 | 0.20 | 0.22 | 1.15 | 0.93 | 0.26 | -0.46 | 0.05 |
| Sn | 22 | 26 | 9.82 | 6.32 | 11.03 | 9.54 | 7.56 | 0.45 | 22.16 | 21.70 | 0.23 | -1.13 | 1.24 |
| Sb | 23 | 26 | 1.14 | 0.99 | 1.11 | 1.00 | 0.92 | 0.10 | 3.90 | 3.79 | 1.21 | 0.97 | 0.19 |
| Cs | 24 | 26 | 1.02 | 1.05 | 0.73 | 0.87 | 0.87 | 0.05 | 3.66 | 3.61 | 1.13 | 0.35 | 0.21 |
| Ba | 25 | 26 | 909.92 | 584.46 | 740.10 | 848.65 | 503.12 | 177.30 | 2249.00 | 2071.70 | 0.90 | -0.26 | 114.62 |
| La | 26 | 26 | 16.52 | 4.60 | 16.09 | 16.10 | 2.74 | 9.29 | 27.99 | 18.70 | 0.90 | 0.66 | 0.90 |
| Ce | 27 | 26 | 36.82 | 9.68 | 37.16 | 36.12 | 5.40 | 18.68 | 61.91 | 43.22 | 0.73 | 0.76 | 1.90 |
| Pr | 28 | 26 | 4.03 | 1.08 | 3.84 | 3.92 | 0.76 | 2.44 | 6.82 | 4.38 | 1.02 | 0.69 | 0.21 |
| Nd | 29 | 26 | 14.75 | 3.91 | 14.06 | 14.37 | 2.51 | 9.11 | 24.48 | 15.36 | 0.99 | 0.57 | 0.77 |
| Sm | 30 | 26 | 2.72 | 0.70 | 2.57 | 2.65 | 0.48 | 1.68 | 4.52 | 2.84 | 1.03 | 0.68 | 0.14 |
| Eu | 31 | 26 | 0.60 | 0.15 | 0.59 | 0.59 | 0.09 | 0.38 | 0.94 | 0.57 | 0.79 | 0.29 | 0.03 |
| Gd | 32 | 26 | 2.13 | 0.61 | 1.98 | 2.08 | 0.38 | 1.15 | 3.65 | 2.50 | 0.90 | 0.48 | 0.12 |
| Tb | 33 | 26 | 0.30 | 0.09 | 0.29 | 0.29 | 0.06 | 0.16 | 0.51 | 0.35 | 0.87 | 0.25 | 0.02 |
| Dy | 34 | 26 | 1.59 | 0.47 | 1.46 | 1.55 | 0.33 | 1.00 | 2.78 | 1.78 | 0.99 | 0.30 | 0.09 |
| Ho | 35 | 26 | 0.31 | 0.09 | 0.29 | 0.30 | 0.08 | 0.17 | 0.52 | 0.36 | 0.75 | -0.13 | 0.02 |
| Er | 36 | 26 | 0.87 | 0.28 | 0.80 | 0.84 | 0.22 | 0.50 | 1.55 | 1.05 | 0.93 | 0.05 | 0.05 |
| Tm | 37 | 26 | 0.12 | 0.04 | 0.11 | 0.12 | 0.04 | 0.06 | 0.22 | 0.15 | 0.76 | -0.38 | 0.01 |
| Yb | 38 | 26 | 0.79 | 0.29 | 0.71 | 0.77 | 0.23 | 0.44 | 1.49 | 1.05 | 0.89 | -0.09 | 0.06 |
| Lu | 39 | 26 | 0.11 | 0.04 | 0.10 | 0.10 | 0.04 | 0.06 | 0.20 | 0.14 | 0.81 | -0.31 | 0.01 |
| Hf | 40 | 26 | 1.12 | 0.74 | 1.03 | 1.06 | 0.79 | 0.18 | 2.69 | 2.50 | 0.63 | -0.75 | 0.15 |
| Ta | 41 | 26 | 0.28 | 0.27 | 0.21 | 0.23 | 0.20 | 0.02 | 1.05 | 1.02 | 1.43 | 1.35 | 0.05 |
| W | 42 | 26 | 1.36 | 1.04 | 1.31 | 1.24 | 1.12 | 0.24 | 4.37 | 4.12 | 1.05 | 0.57 | 0.20 |
| Tl | 43 | 26 | 0.32 | 0.16 | 0.28 | 0.31 | 0.18 | 0.10 | 0.66 | 0.56 | 0.49 | -0.95 | 0.03 |
| Pb | 44 | 26 | 48.53 | 30.99 | 39.98 | 45.85 | 17.85 | 3.92 | 137.07 | 133.15 | 1.12 | 0.74 | 6.08 |
| Bi | 45 | 26 | 0.28 | 0.20 | 0.24 | 0.25 | 0.11 | 0.05 | 0.98 | 0.93 | 1.82 | 3.83 | 0.04 |
| Th | 46 | 26 | 3.14 | 2.42 | 2.45 | 2.80 | 1.81 | 0.90 | 9.42 | 8.52 | 1.22 | 0.58 | 0.47 |
| U | 47 | 26 | 1.13 | 0.87 | 0.79 | 1.04 | 0.64 | 0.28 | 3.15 | 2.88 | 0.72 | -0.85 | 0.17 |
Матрица корреляций.
depth Li Be P Sc Ti V Cr Mn Co Ni
depth 1.00 NA NA NA NA NA NA NA NA NA NA
Li -0.78 1.00 NA NA NA NA NA NA NA NA NA
Be -0.83 0.95 1.00 NA NA NA NA NA NA NA NA
P 0.81 -0.75 -0.75 1.00 NA NA NA NA NA NA NA
Sc -0.62 0.57 0.56 -0.49 1.00 NA NA NA NA NA NA
Ti -0.78 1.00 0.94 -0.74 0.55 1.00 NA NA NA NA NA
V -0.50 0.72 0.68 -0.44 0.41 0.69 1.00 NA NA NA NA
Cr -0.66 0.88 0.86 -0.57 0.47 0.86 0.94 1.00 NA NA NA
Mn 0.80 -0.75 -0.75 0.98 -0.50 -0.73 -0.49 -0.60 1.00 NA NA
Co -0.46 0.52 0.62 -0.19 0.34 0.52 0.42 0.58 -0.16 1.00 NA
Ni -0.59 0.76 0.72 -0.53 0.39 0.74 0.97 0.92 -0.58 0.39 1.00
Cu -0.76 0.50 0.50 -0.58 0.31 0.51 0.51 0.53 -0.55 0.14 0.60
Zn -0.54 0.33 0.36 -0.20 0.14 0.34 0.57 0.50 -0.21 0.27 0.66
Rb -0.74 0.99 0.94 -0.69 0.57 0.99 0.73 0.89 -0.69 0.56 0.76
Sr -0.61 0.78 0.77 -0.37 0.33 0.81 0.42 0.65 -0.31 0.68 0.46
Y -0.77 0.91 0.93 -0.59 0.44 0.92 0.61 0.82 -0.56 0.69 0.65
Zr -0.77 0.84 0.92 -0.59 0.54 0.84 0.56 0.75 -0.60 0.63 0.58
Nb -0.78 0.99 0.96 -0.72 0.56 0.99 0.73 0.89 -0.72 0.55 0.76
Mo -0.39 0.21 0.24 -0.18 0.12 0.19 0.62 0.48 -0.23 0.17 0.68
Ag 0.42 -0.53 -0.44 0.42 -0.50 -0.53 -0.50 -0.48 0.44 0.08 -0.47
Cd -0.50 0.13 0.32 -0.27 0.05 0.12 0.26 0.26 -0.30 0.32 0.33
Sn -0.54 0.17 0.25 -0.28 0.25 0.17 0.34 0.36 -0.29 0.27 0.36
Sb -0.38 0.00 0.22 -0.33 0.22 0.00 -0.06 0.04 -0.35 0.32 -0.03
Cs -0.75 0.99 0.94 -0.71 0.57 0.99 0.75 0.90 -0.71 0.56 0.78
Ba 0.67 -0.60 -0.57 0.87 -0.41 -0.59 -0.41 -0.47 0.91 0.04 -0.50
La -0.65 0.85 0.86 -0.43 0.40 0.87 0.63 0.82 -0.41 0.72 0.63
Ce -0.53 0.78 0.80 -0.32 0.24 0.80 0.58 0.77 -0.30 0.72 0.56
Pr -0.69 0.88 0.88 -0.47 0.51 0.89 0.64 0.82 -0.46 0.70 0.64
Nd -0.69 0.89 0.88 -0.49 0.47 0.90 0.65 0.83 -0.47 0.69 0.65
Sm -0.70 0.89 0.89 -0.51 0.48 0.90 0.63 0.82 -0.49 0.68 0.64
Eu -0.64 0.83 0.85 -0.43 0.45 0.85 0.56 0.77 -0.38 0.72 0.57
Gd -0.69 0.90 0.89 -0.52 0.37 0.91 0.65 0.84 -0.50 0.68 0.67
Tb -0.76 0.92 0.92 -0.59 0.48 0.94 0.69 0.87 -0.57 0.69 0.71
Dy -0.77 0.95 0.94 -0.62 0.55 0.95 0.69 0.88 -0.60 0.65 0.70
Ho -0.79 0.93 0.94 -0.62 0.51 0.94 0.65 0.85 -0.61 0.67 0.68
Er -0.79 0.96 0.95 -0.65 0.53 0.97 0.69 0.87 -0.64 0.63 0.71
Tm -0.79 0.95 0.93 -0.68 0.46 0.96 0.64 0.84 -0.65 0.58 0.67
Yb -0.80 0.96 0.95 -0.68 0.52 0.97 0.67 0.86 -0.66 0.60 0.71
Lu -0.83 0.97 0.95 -0.71 0.58 0.98 0.68 0.86 -0.70 0.60 0.72
Hf -0.81 0.94 0.97 -0.70 0.57 0.95 0.65 0.84 -0.69 0.60 0.68
Ta -0.67 0.95 0.92 -0.61 0.49 0.95 0.80 0.93 -0.63 0.60 0.81
W -0.79 0.50 0.58 -0.68 0.25 0.52 0.22 0.36 -0.65 0.09 0.31
Tl -0.79 0.94 0.95 -0.72 0.52 0.92 0.73 0.89 -0.73 0.62 0.77
Pb -0.04 -0.28 -0.09 0.14 0.00 -0.28 -0.23 -0.16 0.14 0.43 -0.25
Bi -0.13 -0.08 0.11 -0.01 -0.02 -0.08 -0.11 -0.02 -0.04 0.38 -0.11
Th -0.75 0.99 0.94 -0.69 0.57 0.99 0.75 0.90 -0.69 0.56 0.77
U -0.81 0.95 0.90 -0.74 0.55 0.95 0.82 0.92 -0.75 0.44 0.87
Cu Zn Rb Sr Y Zr Nb Mo Ag Cd Sn
depth NA NA NA NA NA NA NA NA NA NA NA
Li NA NA NA NA NA NA NA NA NA NA NA
Be NA NA NA NA NA NA NA NA NA NA NA
P NA NA NA NA NA NA NA NA NA NA NA
Sc NA NA NA NA NA NA NA NA NA NA NA
Ti NA NA NA NA NA NA NA NA NA NA NA
V NA NA NA NA NA NA NA NA NA NA NA
Cr NA NA NA NA NA NA NA NA NA NA NA
Mn NA NA NA NA NA NA NA NA NA NA NA
Co NA NA NA NA NA NA NA NA NA NA NA
Ni NA NA NA NA NA NA NA NA NA NA NA
Cu 1.00 NA NA NA NA NA NA NA NA NA NA
Zn 0.77 1.00 NA NA NA NA NA NA NA NA NA
Rb 0.47 0.33 1.00 NA NA NA NA NA NA NA NA
Sr 0.34 0.35 0.80 1.00 NA NA NA NA NA NA NA
Y 0.53 0.42 0.92 0.92 1.00 NA NA NA NA NA NA
Zr 0.41 0.32 0.84 0.70 0.86 1.00 NA NA NA NA NA
Nb 0.49 0.34 1.00 0.79 0.92 0.87 1.00 NA NA NA NA
Mo 0.67 0.89 0.20 0.08 0.23 0.18 0.20 1.00 NA NA NA
Ag -0.46 -0.22 -0.54 -0.16 -0.35 -0.49 -0.54 -0.21 1.00 NA NA
Cd 0.42 0.58 0.09 0.07 0.21 0.43 0.16 0.57 -0.06 1.00 NA
Sn 0.65 0.56 0.16 0.18 0.29 0.13 0.16 0.57 0.04 0.39 1.00
Sb 0.13 0.01 -0.02 -0.03 0.10 0.18 0.01 0.10 0.37 0.46 0.48
Cs 0.48 0.34 1.00 0.78 0.91 0.85 1.00 0.22 -0.55 0.13 0.16
Ba -0.52 -0.17 -0.55 -0.09 -0.38 -0.50 -0.58 -0.24 0.51 -0.27 -0.15
La 0.45 0.41 0.89 0.92 0.97 0.80 0.87 0.21 -0.33 0.11 0.24
Ce 0.35 0.34 0.82 0.91 0.94 0.75 0.80 0.15 -0.24 0.09 0.18
Pr 0.47 0.40 0.90 0.90 0.97 0.82 0.89 0.22 -0.38 0.09 0.24
Nd 0.49 0.41 0.91 0.92 0.98 0.80 0.90 0.22 -0.36 0.08 0.27
Sm 0.47 0.38 0.91 0.92 0.98 0.80 0.90 0.20 -0.36 0.08 0.26
Eu 0.41 0.36 0.86 0.95 0.96 0.78 0.85 0.15 -0.29 0.08 0.24
Gd 0.48 0.40 0.92 0.91 0.98 0.81 0.91 0.21 -0.35 0.12 0.24
Tb 0.55 0.45 0.94 0.89 0.98 0.84 0.94 0.27 -0.41 0.17 0.30
Dy 0.51 0.39 0.96 0.89 0.98 0.85 0.95 0.24 -0.42 0.14 0.28
Ho 0.54 0.43 0.94 0.89 0.99 0.87 0.94 0.26 -0.40 0.19 0.31
Er 0.54 0.40 0.96 0.88 0.98 0.85 0.96 0.24 -0.45 0.15 0.27
Tm 0.55 0.38 0.94 0.88 0.97 0.84 0.95 0.22 -0.43 0.17 0.29
Yb 0.54 0.39 0.97 0.88 0.98 0.86 0.97 0.21 -0.44 0.15 0.27
Lu 0.54 0.40 0.97 0.84 0.95 0.85 0.97 0.24 -0.47 0.16 0.28
Hf 0.47 0.33 0.94 0.77 0.92 0.97 0.96 0.19 -0.51 0.31 0.18
Ta 0.42 0.33 0.97 0.75 0.88 0.84 0.97 0.23 -0.50 0.16 0.15
W 0.75 0.39 0.45 0.34 0.53 0.60 0.51 0.23 -0.44 0.51 0.36
Tl 0.47 0.39 0.92 0.72 0.88 0.91 0.94 0.31 -0.48 0.38 0.24
Pb -0.11 -0.04 -0.27 -0.08 -0.09 -0.06 -0.26 0.02 0.50 0.39 0.44
Bi -0.16 -0.05 -0.08 0.07 0.08 0.15 -0.06 -0.02 0.57 0.41 0.17
Th 0.49 0.34 1.00 0.81 0.92 0.84 0.99 0.21 -0.52 0.09 0.18
U 0.69 0.55 0.94 0.71 0.88 0.78 0.94 0.44 -0.57 0.22 0.35
Sb Cs Ba La Ce Pr Nd Sm Eu Gd Tb
depth NA NA NA NA NA NA NA NA NA NA NA
Li NA NA NA NA NA NA NA NA NA NA NA
Be NA NA NA NA NA NA NA NA NA NA NA
P NA NA NA NA NA NA NA NA NA NA NA
Sc NA NA NA NA NA NA NA NA NA NA NA
Ti NA NA NA NA NA NA NA NA NA NA NA
V NA NA NA NA NA NA NA NA NA NA NA
Cr NA NA NA NA NA NA NA NA NA NA NA
Mn NA NA NA NA NA NA NA NA NA NA NA
Co NA NA NA NA NA NA NA NA NA NA NA
Ni NA NA NA NA NA NA NA NA NA NA NA
Cu NA NA NA NA NA NA NA NA NA NA NA
Zn NA NA NA NA NA NA NA NA NA NA NA
Rb NA NA NA NA NA NA NA NA NA NA NA
Sr NA NA NA NA NA NA NA NA NA NA NA
Y NA NA NA NA NA NA NA NA NA NA NA
Zr NA NA NA NA NA NA NA NA NA NA NA
Nb NA NA NA NA NA NA NA NA NA NA NA
Mo NA NA NA NA NA NA NA NA NA NA NA
Ag NA NA NA NA NA NA NA NA NA NA NA
Cd NA NA NA NA NA NA NA NA NA NA NA
Sn NA NA NA NA NA NA NA NA NA NA NA
Sb 1.00 NA NA NA NA NA NA NA NA NA NA
Cs -0.01 1.00 NA NA NA NA NA NA NA NA NA
Ba -0.27 -0.57 1.00 NA NA NA NA NA NA NA NA
La 0.00 0.87 -0.23 1.00 NA NA NA NA NA NA NA
Ce -0.04 0.80 -0.12 0.98 1.00 NA NA NA NA NA NA
Pr 0.03 0.89 -0.29 0.99 0.95 1.00 NA NA NA NA NA
Nd 0.02 0.90 -0.29 0.99 0.96 0.99 1.00 NA NA NA NA
Sm 0.04 0.90 -0.29 0.99 0.95 0.99 1.00 1.00 NA NA NA
Eu 0.03 0.85 -0.16 0.98 0.95 0.97 0.98 0.98 1.00 NA NA
Gd 0.03 0.91 -0.33 0.99 0.96 0.97 0.99 0.98 0.96 1.00 NA
Tb 0.06 0.93 -0.40 0.98 0.93 0.98 0.99 0.98 0.95 0.98 1.00
Dy 0.08 0.95 -0.42 0.96 0.90 0.97 0.98 0.98 0.95 0.97 0.98
Ho 0.10 0.93 -0.43 0.96 0.91 0.97 0.98 0.98 0.94 0.97 0.99
Er 0.06 0.96 -0.46 0.95 0.90 0.97 0.97 0.97 0.94 0.97 0.99
Tm 0.05 0.94 -0.47 0.92 0.87 0.92 0.94 0.94 0.91 0.95 0.96
Yb 0.07 0.96 -0.48 0.94 0.88 0.95 0.96 0.96 0.93 0.97 0.98
Lu 0.08 0.97 -0.54 0.91 0.83 0.92 0.93 0.93 0.89 0.93 0.96
Hf 0.13 0.95 -0.57 0.86 0.79 0.87 0.87 0.87 0.84 0.88 0.91
Ta 0.00 0.97 -0.49 0.87 0.83 0.87 0.88 0.88 0.83 0.90 0.91
W 0.27 0.46 -0.63 0.39 0.33 0.40 0.41 0.42 0.37 0.45 0.48
Tl 0.11 0.94 -0.58 0.80 0.75 0.81 0.82 0.82 0.78 0.84 0.87
Pb 0.59 -0.26 0.27 -0.11 -0.08 -0.12 -0.13 -0.13 -0.07 -0.16 -0.12
Bi 0.79 -0.08 0.00 0.05 0.08 0.04 0.02 0.05 0.06 0.06 0.02
Th -0.01 1.00 -0.53 0.89 0.83 0.91 0.92 0.92 0.87 0.93 0.95
U 0.01 0.95 -0.63 0.83 0.74 0.85 0.86 0.86 0.79 0.87 0.91
Dy Ho Er Tm Yb Lu Hf Ta W Tl Pb
depth NA NA NA NA NA NA NA NA NA NA NA
Li NA NA NA NA NA NA NA NA NA NA NA
Be NA NA NA NA NA NA NA NA NA NA NA
P NA NA NA NA NA NA NA NA NA NA NA
Sc NA NA NA NA NA NA NA NA NA NA NA
Ti NA NA NA NA NA NA NA NA NA NA NA
V NA NA NA NA NA NA NA NA NA NA NA
Cr NA NA NA NA NA NA NA NA NA NA NA
Mn NA NA NA NA NA NA NA NA NA NA NA
Co NA NA NA NA NA NA NA NA NA NA NA
Ni NA NA NA NA NA NA NA NA NA NA NA
Cu NA NA NA NA NA NA NA NA NA NA NA
Zn NA NA NA NA NA NA NA NA NA NA NA
Rb NA NA NA NA NA NA NA NA NA NA NA
Sr NA NA NA NA NA NA NA NA NA NA NA
Y NA NA NA NA NA NA NA NA NA NA NA
Zr NA NA NA NA NA NA NA NA NA NA NA
Nb NA NA NA NA NA NA NA NA NA NA NA
Mo NA NA NA NA NA NA NA NA NA NA NA
Ag NA NA NA NA NA NA NA NA NA NA NA
Cd NA NA NA NA NA NA NA NA NA NA NA
Sn NA NA NA NA NA NA NA NA NA NA NA
Sb NA NA NA NA NA NA NA NA NA NA NA
Cs NA NA NA NA NA NA NA NA NA NA NA
Ba NA NA NA NA NA NA NA NA NA NA NA
La NA NA NA NA NA NA NA NA NA NA NA
Ce NA NA NA NA NA NA NA NA NA NA NA
Pr NA NA NA NA NA NA NA NA NA NA NA
Nd NA NA NA NA NA NA NA NA NA NA NA
Sm NA NA NA NA NA NA NA NA NA NA NA
Eu NA NA NA NA NA NA NA NA NA NA NA
Gd NA NA NA NA NA NA NA NA NA NA NA
Tb NA NA NA NA NA NA NA NA NA NA NA
Dy 1.00 NA NA NA NA NA NA NA NA NA NA
Ho 0.98 1.00 NA NA NA NA NA NA NA NA NA
Er 0.99 0.99 1.00 NA NA NA NA NA NA NA NA
Tm 0.97 0.97 0.98 1.00 NA NA NA NA NA NA NA
Yb 0.99 0.98 0.99 0.98 1.00 NA NA NA NA NA NA
Lu 0.97 0.97 0.98 0.96 0.98 1.00 NA NA NA NA NA
Hf 0.93 0.93 0.93 0.93 0.94 0.94 1.00 NA NA NA NA
Ta 0.92 0.91 0.92 0.89 0.93 0.93 0.92 1.00 NA NA NA
W 0.48 0.51 0.51 0.56 0.54 0.52 0.59 0.40 1.00 NA NA
Tl 0.89 0.89 0.90 0.91 0.91 0.91 0.96 0.92 0.54 1.00 NA
Pb -0.16 -0.10 -0.19 -0.19 -0.19 -0.20 -0.15 -0.23 -0.11 -0.09 1.00
Bi 0.04 0.04 0.00 -0.01 0.01 -0.01 0.07 -0.01 0.05 0.03 0.46
Th 0.97 0.95 0.97 0.96 0.97 0.98 0.94 0.97 0.46 0.92 -0.27
U 0.92 0.91 0.93 0.92 0.93 0.94 0.89 0.91 0.56 0.90 -0.31
Bi Th U
depth NA NA NA
Li NA NA NA
Be NA NA NA
P NA NA NA
Sc NA NA NA
Ti NA NA NA
V NA NA NA
Cr NA NA NA
Mn NA NA NA
Co NA NA NA
Ni NA NA NA
Cu NA NA NA
Zn NA NA NA
Rb NA NA NA
Sr NA NA NA
Y NA NA NA
Zr NA NA NA
Nb NA NA NA
Mo NA NA NA
Ag NA NA NA
Cd NA NA NA
Sn NA NA NA
Sb NA NA NA
Cs NA NA NA
Ba NA NA NA
La NA NA NA
Ce NA NA NA
Pr NA NA NA
Nd NA NA NA
Sm NA NA NA
Eu NA NA NA
Gd NA NA NA
Tb NA NA NA
Dy NA NA NA
Ho NA NA NA
Er NA NA NA
Tm NA NA NA
Yb NA NA NA
Lu NA NA NA
Hf NA NA NA
Ta NA NA NA
W NA NA NA
Tl NA NA NA
Pb NA NA NA
Bi 1.00 NA NA
Th -0.07 1.00 NA
U -0.11 0.95 1Показываем только больше 0,5
Scree plot
Сколько факторов выбрать?
In factor.scores, the correlation matrix is singular, an approximation is used
Общие рекомендации:
To select as many factors as there are eigenvalues larger than the average;
To select enough factors to reach a certain preselected explained variance (e.g. >70%);
To use the scree plot (Cattell, 1966) where the number of factors is plotted against explained variance and the cutoff is chosen at the point where the function flattens out.
link, C. 13
Factor analysis
2 factors
Проведём анализ с 2 факторами.
In factor.scores, the correlation matrix is singular, an approximation is usedFactor Analysis using method = minres
Call: fa(r = lake2, nfactors = 2)
Warning: A Heywood case was detected.
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR2 h2 u2 com
depth -0.44 -0.65 0.877 0.1232 1.7
Li 0.87 0.18 0.941 0.0585 1.1
Be 0.83 0.25 0.937 0.0632 1.2
P -0.29 -0.66 0.699 0.3009 1.4
Sc 0.38 0.27 0.314 0.6857 1.8
Ti 0.89 0.16 0.950 0.0495 1.1
V 0.54 0.33 0.568 0.4317 1.7
Cr 0.76 0.25 0.824 0.1764 1.2
Mn -0.25 -0.71 0.738 0.2623 1.2
Co 0.73 -0.18 0.445 0.5550 1.1
Ni 0.51 0.44 0.657 0.3427 2.0
Cu 0.14 0.73 0.643 0.3568 1.1
Zn 0.15 0.50 0.337 0.6629 1.2
Rb 0.92 0.10 0.951 0.0487 1.0
Sr 1.02 -0.29 0.847 0.1530 1.2
Y 0.97 0.01 0.959 0.0411 1.0
Zr 0.77 0.19 0.768 0.2319 1.1
Nb 0.89 0.16 0.956 0.0445 1.1
Mo -0.07 0.61 0.343 0.6569 1.0
Ag -0.29 -0.32 0.271 0.7288 2.0
Cd -0.16 0.64 0.342 0.6584 1.1
Sn -0.02 0.52 0.264 0.7364 1.0
Sb -0.16 0.41 0.130 0.8696 1.3
Cs 0.90 0.14 0.949 0.0507 1.1
Ba -0.06 -0.76 0.627 0.3733 1.0
La 1.04 -0.17 0.954 0.0459 1.1
Ce 1.05 -0.29 0.905 0.0949 1.2
Pr 1.03 -0.12 0.955 0.0452 1.0
Nd 1.03 -0.11 0.968 0.0320 1.0
Sm 1.03 -0.11 0.965 0.0347 1.0
Eu 1.05 -0.22 0.934 0.0660 1.1
Gd 1.02 -0.08 0.962 0.0379 1.0
Tb 0.97 0.03 0.977 0.0232 1.0
Dy 0.98 0.04 0.987 0.0133 1.0
Ho 0.96 0.07 0.976 0.0244 1.0
Er 0.96 0.07 0.991 0.0088 1.0
Tm 0.92 0.10 0.949 0.0505 1.0
Yb 0.95 0.09 0.985 0.0146 1.0
Lu 0.90 0.16 0.969 0.0306 1.1
Hf 0.84 0.20 0.915 0.0854 1.1
Ta 0.91 0.08 0.896 0.1039 1.0
W 0.16 0.64 0.530 0.4703 1.1
Tl 0.77 0.29 0.887 0.1134 1.3
Pb -0.20 0.05 0.032 0.9680 1.1
Bi -0.02 0.05 0.002 0.9980 1.4
Th 0.93 0.10 0.963 0.0369 1.0
U 0.74 0.38 0.952 0.0482 1.5
MR1 MR2
SS loadings 28.1 6.89
Proportion Var 0.6 0.15
Cumulative Var 0.6 0.74
Proportion Explained 0.8 0.20
Cumulative Proportion 0.8 1.00
With factor correlations of
MR1 MR2
MR1 1.00 0.47
MR2 0.47 1.00
Mean item complexity = 1.2
Test of the hypothesis that 2 factors are sufficient.
The degrees of freedom for the null model are 1081 and the objective function was 557.94 with Chi Square of 4742.49
The degrees of freedom for the model are 988 and the objective function was 464.04
The root mean square of the residuals (RMSR) is 0.09
The df corrected root mean square of the residuals is 0.1
The harmonic number of observations is 26 with the empirical chi square 469.54 with prob < 1
The total number of observations was 26 with Likelihood Chi Square = 3325.65 with prob < 4.6e-250
Tucker Lewis Index of factoring reliability = 0.123
RMSEA index = 0.655 and the 90 % confidence intervals are 0.296 NA
BIC = 106.65
Fit based upon off diagonal values = 0.98Каждый объединяет хим элементы следующим образом:
Loadings:
MR1 MR2
depth -0.435 -0.649
Li 0.871 0.182
Be 0.826 0.249
P -0.289 -0.660
Sc 0.383 0.268
Ti 0.892 0.156
V 0.540 0.330
Cr 0.760 0.254
Mn -0.253 -0.710
Co 0.732 -0.179
Ni 0.506 0.439
Cu 0.141 0.726
Zn 0.148 0.496
Rb 0.924 0.101
Sr 1.020 -0.287
Y 0.973
Zr 0.770 0.191
Nb 0.891 0.162
Mo 0.614
Ag -0.286 -0.321
Cd -0.157 0.642
Sn 0.523
Sb -0.165 0.408
Cs 0.898 0.144
Ba -0.764
La 1.045 -0.168
Ce 1.053 -0.291
Pr 1.027 -0.117
Nd 1.031 -0.111
Sm 1.030 -0.110
Eu 1.049 -0.216
Gd 1.018
Tb 0.974
Dy 0.976
Ho 0.955
Er 0.960
Tm 0.923 0.101
Yb 0.947
Lu 0.899 0.160
Hf 0.843 0.205
Ta 0.905
W 0.159 0.639
Tl 0.767 0.293
Pb -0.196
Bi
Th 0.928 0.104
U 0.737 0.380
MR1 MR2
SS loadings 26.991 5.779
Proportion Var 0.574 0.123
Cumulative Var 0.574 0.6971 фактор описывает данные на 57.4%
1+2 факторы описывают данные на 69.7% 
2D репрезентация исходных наблюдений в новом пространстве факторов. 
О том, почему некоторые элементы имеют loadings выше 1:
This misunderstanding probably stems from classical exploratory factor analysis where factor loadings are correlations if a correlation matrix is analyzed and the factors are standardized and uncorrelated (orthogonal). However, if the factors are correlated (oblique), the factor loadings are regression coefficients and not correlations and as such they can be larger than one in magnitude. link
3 factors
Проведём анализ с 3 факторами.
In factor.scores, the correlation matrix is singular, an approximation is usedFactor Analysis using method = minres
Call: fa(r = lake2, nfactors = 3)
Warning: A Heywood case was detected.
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR2 MR3 h2 u2 com
depth -0.50 -0.63 -0.20 0.91 0.0945 2.1
Li 0.86 0.18 -0.20 0.98 0.0242 1.2
Be 0.85 0.24 0.04 0.94 0.0606 1.2
P -0.32 -0.64 0.10 0.72 0.2805 1.5
Sc 0.39 0.26 -0.05 0.32 0.6819 1.8
Ti 0.88 0.16 -0.19 0.98 0.0195 1.2
V 0.55 0.32 -0.12 0.58 0.4180 1.7
Cr 0.77 0.25 -0.04 0.82 0.1764 1.2
Mn -0.29 -0.69 0.11 0.76 0.2375 1.4
Co 0.80 -0.20 0.53 0.79 0.2078 1.9
Ni 0.53 0.42 -0.11 0.67 0.3312 2.0
Cu 0.20 0.69 0.07 0.63 0.3681 1.2
Zn 0.21 0.47 0.21 0.36 0.6363 1.8
Rb 0.91 0.10 -0.20 0.98 0.0190 1.1
Sr 1.01 -0.28 0.11 0.88 0.1201 1.2
Y 0.98 0.01 0.10 0.98 0.0229 1.0
Zr 0.79 0.19 0.07 0.78 0.2245 1.1
Nb 0.88 0.16 -0.17 0.98 0.0211 1.1
Mo 0.00 0.59 0.20 0.36 0.6414 1.2
Ag -0.24 -0.34 0.59 0.65 0.3521 2.0
Cd -0.07 0.65 0.53 0.60 0.4026 2.0
Sn 0.06 0.52 0.50 0.49 0.5094 2.0
Sb -0.08 0.44 0.72 0.62 0.3772 1.7
Cs 0.89 0.15 -0.19 0.98 0.0211 1.2
Ba -0.08 -0.76 0.24 0.73 0.2711 1.2
La 1.04 -0.16 0.07 0.97 0.0294 1.1
Ce 1.04 -0.28 0.10 0.93 0.0659 1.2
Pr 1.02 -0.11 0.04 0.96 0.0371 1.0
Nd 1.03 -0.11 0.04 0.98 0.0247 1.0
Sm 1.03 -0.10 0.04 0.97 0.0271 1.0
Eu 1.05 -0.21 0.10 0.96 0.0405 1.1
Gd 1.02 -0.08 0.04 0.97 0.0315 1.0
Tb 0.98 0.03 0.04 0.98 0.0176 1.0
Dy 0.98 0.04 0.00 0.99 0.0127 1.0
Ho 0.97 0.07 0.06 0.98 0.0168 1.0
Er 0.96 0.07 -0.03 0.99 0.0097 1.0
Tm 0.92 0.10 -0.04 0.95 0.0513 1.0
Yb 0.95 0.09 -0.04 0.98 0.0154 1.0
Lu 0.90 0.16 -0.06 0.97 0.0298 1.1
Hf 0.85 0.20 -0.03 0.91 0.0859 1.1
Ta 0.89 0.08 -0.14 0.91 0.0922 1.1
W 0.21 0.62 0.06 0.53 0.4728 1.3
Tl 0.79 0.29 -0.01 0.89 0.1142 1.3
Pb -0.11 0.05 0.78 0.63 0.3729 1.1
Bi 0.05 0.05 0.70 0.48 0.5178 1.0
Th 0.92 0.11 -0.18 0.99 0.0133 1.1
U 0.75 0.37 -0.17 0.98 0.0207 1.6
MR1 MR2 MR3
SS loadings 28.37 6.65 3.36
Proportion Var 0.60 0.14 0.07
Cumulative Var 0.60 0.75 0.82
Proportion Explained 0.74 0.17 0.09
Cumulative Proportion 0.74 0.91 1.00
With factor correlations of
MR1 MR2 MR3
MR1 1.00 0.41 -0.07
MR2 0.41 1.00 -0.11
MR3 -0.07 -0.11 1.00
Mean item complexity = 1.3
Test of the hypothesis that 3 factors are sufficient.
The degrees of freedom for the null model are 1081 and the objective function was 557.94 with Chi Square of 4742.49
The degrees of freedom for the model are 943 and the objective function was 450.8
The root mean square of the residuals (RMSR) is 0.06
The df corrected root mean square of the residuals is 0.07
The harmonic number of observations is 26 with the empirical chi square 219.75 with prob < 1
The total number of observations was 26 with Likelihood Chi Square = 2930.18 with prob < 3.9e-202
Tucker Lewis Index of factoring reliability = 0.105
RMSEA index = 0.662 and the 90 % confidence intervals are 0.278 NA
BIC = -142.2
Fit based upon off diagonal values = 0.99Каждый объединяет хим элементы следующим образом:
Loadings:
MR1 MR2 MR3
depth -0.504 -0.630 -0.199
Li 0.861 0.182 -0.203
Be 0.847 0.244
P -0.323 -0.645 0.102
Sc 0.394 0.263
Ti 0.881 0.157 -0.195
V 0.552 0.319 -0.121
Cr 0.774 0.246
Mn -0.289 -0.694 0.109
Co 0.798 -0.200 0.527
Ni 0.528 0.423 -0.109
Cu 0.205 0.695
Zn 0.210 0.473 0.208
Rb 0.908 0.104 -0.199
Sr 1.014 -0.278 0.114
Y 0.985
Zr 0.790 0.189
Nb 0.882 0.162 -0.175
Mo 0.586 0.200
Ag -0.236 -0.339 0.589
Cd 0.648 0.531
Sn 0.522 0.502
Sb 0.436 0.720
Cs 0.886 0.145 -0.195
Ba -0.759 0.236
La 1.041 -0.161
Ce 1.045 -0.282 0.102
Pr 1.022 -0.110
Nd 1.027 -0.105
Sm 1.026 -0.104
Eu 1.045 -0.208
Gd 1.015
Tb 0.980
Dy 0.978
Ho 0.965
Er 0.960
Tm 0.925 0.101
Yb 0.948
Lu 0.903 0.158
Hf 0.852 0.203
Ta 0.895 -0.139
W 0.213 0.618
Tl 0.786 0.286
Pb -0.114 0.783
Bi 0.698
Th 0.915 0.106 -0.181
U 0.746 0.371 -0.167
MR1 MR2 MR3
SS loadings 27.214 5.569 3.360
Proportion Var 0.579 0.118 0.071
Cumulative Var 0.579 0.697 0.7691 фактор описывает данные на 57.9%
1+2 факторы описывают данные на 69.7%
1+2+3 факторы описывают данные на 76.9% 
3D репрезентация исходных наблюдений в новом пространстве факторов.
О том, почему некоторые элементы имеют loadings выше 1:
This misunderstanding probably stems from classical exploratory factor analysis where factor loadings are correlations if a correlation matrix is analyzed and the factors are standardized and uncorrelated (orthogonal). However, if the factors are correlated (oblique), the factor loadings are regression coefficients and not correlations and as such they can be larger than one in magnitude. link
Lake 3
Describe data
Опишем имеющиеся данные:| vars | n | mean | sd | median | trimmed | mad | min | max | range | skew | kurtosis | se | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| depth | 1 | 13 | 13.08 | 7.92 | 13.00 | 13.00 | 8.90 | 1.00 | 26.00 | 25.00 | 0.05 | -1.43 | 2.20 |
| Li | 2 | 13 | 2.39 | 0.87 | 2.02 | 2.33 | 0.59 | 1.44 | 4.05 | 2.61 | 0.79 | -0.84 | 0.24 |
| Be | 3 | 13 | 0.33 | 0.05 | 0.34 | 0.33 | 0.07 | 0.26 | 0.39 | 0.14 | -0.31 | -1.64 | 0.01 |
| P | 4 | 13 | 1325.77 | 234.64 | 1289.00 | 1301.64 | 210.53 | 1058.00 | 1859.00 | 801.00 | 0.92 | -0.25 | 65.08 |
| Sc | 5 | 13 | 14.04 | 1.78 | 13.78 | 14.16 | 2.25 | 10.37 | 16.30 | 5.93 | -0.44 | -0.97 | 0.49 |
| Ti | 6 | 13 | 515.14 | 101.53 | 504.20 | 509.22 | 82.73 | 363.80 | 731.60 | 367.80 | 0.71 | -0.44 | 28.16 |
| V | 7 | 13 | 22.19 | 11.22 | 16.14 | 20.72 | 3.28 | 13.65 | 46.96 | 33.31 | 1.00 | -0.59 | 3.11 |
| Cr | 8 | 13 | 15.59 | 3.37 | 13.51 | 15.35 | 2.16 | 12.05 | 21.79 | 9.74 | 0.65 | -1.23 | 0.93 |
| Mn | 9 | 13 | 79.71 | 8.89 | 81.97 | 79.69 | 11.93 | 65.38 | 94.19 | 28.81 | 0.01 | -1.46 | 2.47 |
| Co | 10 | 13 | 2.16 | 0.38 | 1.97 | 2.13 | 0.20 | 1.81 | 2.89 | 1.08 | 0.76 | -1.17 | 0.11 |
| Ni | 11 | 13 | 16.58 | 4.64 | 14.64 | 16.31 | 3.81 | 11.71 | 24.36 | 12.65 | 0.54 | -1.40 | 1.29 |
| Cu | 12 | 13 | 31.82 | 7.96 | 30.66 | 30.53 | 5.46 | 23.64 | 54.23 | 30.59 | 1.56 | 2.03 | 2.21 |
| Zn | 13 | 13 | 88.59 | 57.08 | 57.68 | 82.96 | 24.42 | 39.96 | 199.20 | 159.24 | 0.91 | -0.82 | 15.83 |
| Rb | 14 | 13 | 7.96 | 2.62 | 6.95 | 7.81 | 2.73 | 4.80 | 12.73 | 7.94 | 0.49 | -1.30 | 0.73 |
| Sr | 15 | 13 | 31.90 | 4.88 | 29.88 | 31.67 | 4.28 | 26.41 | 39.92 | 13.51 | 0.48 | -1.59 | 1.35 |
| Y | 16 | 13 | 5.87 | 1.02 | 5.95 | 5.89 | 0.81 | 3.98 | 7.53 | 3.55 | -0.09 | -0.96 | 0.28 |
| Zr | 17 | 13 | 38.65 | 26.06 | 28.89 | 37.27 | 19.82 | 9.83 | 82.70 | 72.87 | 0.53 | -1.46 | 7.23 |
| Nb | 18 | 13 | 1.32 | 0.30 | 1.24 | 1.30 | 0.21 | 0.88 | 1.94 | 1.06 | 0.71 | -0.66 | 0.08 |
| Mo | 19 | 13 | 0.93 | 0.19 | 0.86 | 0.92 | 0.09 | 0.71 | 1.33 | 0.62 | 0.90 | -0.72 | 0.05 |
| Ag | 20 | 13 | 0.51 | 0.15 | 0.51 | 0.50 | 0.13 | 0.31 | 0.84 | 0.53 | 0.72 | -0.34 | 0.04 |
| Cd | 21 | 13 | 0.75 | 0.34 | 0.69 | 0.74 | 0.40 | 0.30 | 1.32 | 1.02 | 0.29 | -1.45 | 0.09 |
| Sn | 22 | 13 | 1.71 | 1.43 | 0.85 | 1.61 | 0.70 | 0.38 | 4.18 | 3.80 | 0.56 | -1.47 | 0.40 |
| Sb | 23 | 13 | 0.59 | 0.39 | 0.45 | 0.58 | 0.47 | 0.10 | 1.14 | 1.04 | 0.24 | -1.74 | 0.11 |
| Cs | 24 | 13 | 0.52 | 0.16 | 0.46 | 0.51 | 0.15 | 0.34 | 0.82 | 0.48 | 0.59 | -1.16 | 0.04 |
| Ba | 25 | 13 | 95.77 | 14.97 | 91.60 | 95.21 | 14.08 | 77.95 | 119.80 | 41.85 | 0.44 | -1.49 | 4.15 |
| La | 26 | 13 | 8.15 | 0.50 | 8.26 | 8.19 | 0.63 | 7.10 | 8.77 | 1.67 | -0.43 | -0.81 | 0.14 |
| Ce | 27 | 13 | 15.38 | 1.02 | 15.13 | 15.40 | 0.80 | 13.49 | 17.05 | 3.56 | 0.09 | -1.03 | 0.28 |
| Pr | 28 | 13 | 1.82 | 0.14 | 1.79 | 1.82 | 0.09 | 1.54 | 2.06 | 0.51 | -0.03 | -0.66 | 0.04 |
| Nd | 29 | 13 | 6.73 | 0.49 | 6.60 | 6.73 | 0.40 | 5.93 | 7.55 | 1.61 | 0.28 | -1.21 | 0.14 |
| Sm | 30 | 13 | 1.46 | 0.14 | 1.50 | 1.47 | 0.13 | 1.16 | 1.66 | 0.51 | -0.61 | -0.67 | 0.04 |
| Eu | 31 | 13 | 0.32 | 0.03 | 0.32 | 0.32 | 0.04 | 0.25 | 0.37 | 0.12 | -0.54 | -0.82 | 0.01 |
| Gd | 32 | 13 | 1.28 | 0.16 | 1.33 | 1.28 | 0.14 | 0.97 | 1.53 | 0.56 | -0.37 | -0.91 | 0.04 |
| Tb | 33 | 13 | 0.22 | 0.04 | 0.22 | 0.22 | 0.02 | 0.16 | 0.30 | 0.14 | 0.19 | -1.03 | 0.01 |
| Dy | 34 | 13 | 1.28 | 0.28 | 1.21 | 1.28 | 0.22 | 0.82 | 1.70 | 0.88 | 0.11 | -1.31 | 0.08 |
| Ho | 35 | 13 | 0.25 | 0.06 | 0.24 | 0.25 | 0.05 | 0.16 | 0.34 | 0.19 | 0.09 | -1.35 | 0.02 |
| Er | 36 | 13 | 0.70 | 0.16 | 0.67 | 0.71 | 0.14 | 0.45 | 0.95 | 0.50 | 0.05 | -1.21 | 0.04 |
| Tm | 37 | 13 | 0.09 | 0.01 | 0.08 | 0.08 | 0.01 | 0.06 | 0.11 | 0.05 | 0.29 | -1.12 | 0.00 |
| Yb | 38 | 13 | 0.54 | 0.07 | 0.56 | 0.55 | 0.06 | 0.39 | 0.61 | 0.22 | -0.81 | -0.80 | 0.02 |
| Lu | 39 | 13 | 0.07 | 0.01 | 0.07 | 0.07 | 0.01 | 0.05 | 0.08 | 0.03 | -0.30 | -1.19 | 0.00 |
| Hf | 40 | 13 | 0.94 | 0.58 | 0.72 | 0.90 | 0.46 | 0.30 | 1.94 | 1.65 | 0.52 | -1.44 | 0.16 |
| Ta | 41 | 13 | 0.06 | 0.03 | 0.04 | 0.06 | 0.04 | 0.02 | 0.11 | 0.09 | 0.49 | -1.19 | 0.01 |
| W | 42 | 13 | 0.46 | 0.35 | 0.23 | 0.44 | 0.12 | 0.15 | 1.07 | 0.92 | 0.62 | -1.50 | 0.10 |
| Tl | 43 | 13 | 0.11 | 0.05 | 0.10 | 0.11 | 0.05 | 0.05 | 0.20 | 0.15 | 0.45 | -1.46 | 0.01 |
| Pb | 44 | 13 | 31.02 | 23.50 | 24.85 | 30.64 | 29.06 | 3.19 | 63.13 | 59.94 | 0.14 | -1.90 | 6.52 |
| Bi | 45 | 13 | 0.15 | 0.09 | 0.13 | 0.15 | 0.10 | 0.04 | 0.27 | 0.23 | 0.18 | -1.82 | 0.02 |
| Th | 46 | 13 | 1.74 | 0.17 | 1.67 | 1.73 | 0.10 | 1.47 | 2.07 | 0.61 | 0.53 | -0.91 | 0.05 |
| U | 47 | 13 | 0.52 | 0.05 | 0.52 | 0.52 | 0.06 | 0.46 | 0.60 | 0.14 | 0.05 | -1.61 | 0.01 |
Матрица корреляций.
depth Li Be P Sc Ti V Cr Mn Co Ni
depth 1.00 NA NA NA NA NA NA NA NA NA NA
Li -0.77 1.00 NA NA NA NA NA NA NA NA NA
Be -0.02 0.40 1.00 NA NA NA NA NA NA NA NA
P -0.40 0.04 0.22 1.00 NA NA NA NA NA NA NA
Sc 0.95 -0.66 -0.04 -0.47 1.00 NA NA NA NA NA NA
Ti -0.72 0.96 0.42 0.04 -0.58 1.00 NA NA NA NA NA
V -0.81 0.68 0.33 0.69 -0.80 0.63 1.00 NA NA NA NA
Cr -0.80 0.99 0.44 0.14 -0.69 0.94 0.74 1.00 NA NA NA
Mn -0.95 0.83 0.04 0.25 -0.91 0.78 0.76 0.81 1.00 NA NA
Co -0.81 0.79 0.46 0.58 -0.82 0.76 0.91 0.82 0.81 1.00 NA
Ni -0.91 0.86 0.32 0.47 -0.86 0.80 0.93 0.89 0.90 0.92 1.00
Cu -0.32 0.42 0.51 0.53 -0.34 0.48 0.64 0.43 0.41 0.73 0.58
Zn -0.89 0.66 0.25 0.69 -0.92 0.59 0.96 0.72 0.82 0.91 0.92
Rb -0.84 0.98 0.35 0.08 -0.74 0.93 0.70 0.99 0.86 0.79 0.87
Sr -0.93 0.90 0.32 0.43 -0.88 0.84 0.90 0.91 0.92 0.95 0.97
Y 0.85 -0.35 0.42 -0.41 0.85 -0.28 -0.58 -0.38 -0.75 -0.48 -0.61
Zr -0.84 0.89 0.40 0.16 -0.78 0.86 0.68 0.90 0.85 0.81 0.86
Nb -0.68 0.96 0.40 -0.09 -0.54 0.98 0.54 0.93 0.76 0.69 0.75
Mo -0.74 0.57 0.39 0.82 -0.78 0.53 0.93 0.63 0.67 0.93 0.84
Ag 0.23 -0.14 0.23 0.30 0.34 -0.03 0.01 -0.11 -0.24 0.01 -0.03
Cd -0.96 0.71 0.09 0.46 -0.95 0.63 0.84 0.77 0.88 0.79 0.92
Sn -0.89 0.90 0.36 0.38 -0.83 0.83 0.92 0.93 0.88 0.91 0.99
Sb -0.94 0.93 0.28 0.28 -0.86 0.87 0.83 0.96 0.92 0.87 0.95
Cs -0.79 0.98 0.36 -0.01 -0.67 0.94 0.62 0.98 0.82 0.73 0.83
Ba -0.91 0.93 0.31 0.29 -0.85 0.87 0.82 0.94 0.92 0.89 0.93
La 0.46 0.18 0.62 -0.44 0.54 0.24 -0.25 0.14 -0.33 -0.09 -0.17
Ce 0.08 0.53 0.62 -0.47 0.18 0.54 -0.02 0.49 0.05 0.17 0.18
Pr 0.01 0.59 0.57 -0.50 0.14 0.59 0.01 0.55 0.11 0.16 0.22
Nd -0.08 0.63 0.51 -0.53 0.01 0.63 0.01 0.58 0.22 0.22 0.27
Sm 0.69 -0.13 0.28 -0.58 0.71 -0.09 -0.53 -0.19 -0.52 -0.37 -0.47
Eu 0.55 0.06 0.52 -0.62 0.58 0.09 -0.44 0.01 -0.40 -0.25 -0.32
Gd 0.58 0.00 0.56 -0.44 0.62 0.05 -0.36 -0.03 -0.46 -0.21 -0.29
Tb 0.87 -0.43 0.40 -0.39 0.85 -0.38 -0.62 -0.45 -0.79 -0.53 -0.65
Dy 0.92 -0.53 0.29 -0.33 0.91 -0.44 -0.65 -0.56 -0.84 -0.58 -0.73
Ho 0.93 -0.55 0.29 -0.31 0.93 -0.47 -0.66 -0.56 -0.87 -0.61 -0.73
Er 0.90 -0.47 0.35 -0.37 0.89 -0.39 -0.65 -0.49 -0.83 -0.55 -0.70
Tm 0.89 -0.47 0.35 -0.35 0.86 -0.44 -0.63 -0.49 -0.82 -0.56 -0.68
Yb 0.66 -0.10 0.35 -0.58 0.73 -0.01 -0.55 -0.14 -0.56 -0.38 -0.49
Lu 0.32 0.31 0.57 -0.53 0.40 0.35 -0.21 0.26 -0.14 -0.01 -0.07
Hf -0.84 0.89 0.40 0.17 -0.79 0.87 0.69 0.91 0.86 0.82 0.87
Ta -0.80 0.96 0.39 0.06 -0.71 0.95 0.66 0.95 0.85 0.80 0.84
W -0.89 0.86 0.39 0.51 -0.87 0.81 0.94 0.89 0.88 0.97 0.98
Tl -0.90 0.95 0.34 0.25 -0.83 0.90 0.83 0.96 0.93 0.90 0.96
Pb -0.93 0.92 0.25 0.21 -0.87 0.85 0.78 0.94 0.92 0.83 0.94
Bi -0.93 0.93 0.26 0.21 -0.85 0.87 0.79 0.95 0.92 0.83 0.94
Th -0.18 0.71 0.52 -0.44 0.01 0.77 0.08 0.66 0.28 0.26 0.31
U 0.34 0.16 0.59 -0.15 0.49 0.31 -0.14 0.14 -0.28 0.01 -0.13
Cu Zn Rb Sr Y Zr Nb Mo Ag Cd Sn
depth NA NA NA NA NA NA NA NA NA NA NA
Li NA NA NA NA NA NA NA NA NA NA NA
Be NA NA NA NA NA NA NA NA NA NA NA
P NA NA NA NA NA NA NA NA NA NA NA
Sc NA NA NA NA NA NA NA NA NA NA NA
Ti NA NA NA NA NA NA NA NA NA NA NA
V NA NA NA NA NA NA NA NA NA NA NA
Cr NA NA NA NA NA NA NA NA NA NA NA
Mn NA NA NA NA NA NA NA NA NA NA NA
Co NA NA NA NA NA NA NA NA NA NA NA
Ni NA NA NA NA NA NA NA NA NA NA NA
Cu 1.00 NA NA NA NA NA NA NA NA NA NA
Zn 0.52 1.00 NA NA NA NA NA NA NA NA NA
Rb 0.34 0.71 1.00 NA NA NA NA NA NA NA NA
Sr 0.55 0.91 0.91 1.00 NA NA NA NA NA NA NA
Y -0.01 -0.72 -0.46 -0.62 1.00 NA NA NA NA NA NA
Zr 0.46 0.73 0.93 0.89 -0.49 1.00 NA NA NA NA NA
Nb 0.40 0.51 0.94 0.79 -0.24 0.86 1.00 NA NA NA NA
Mo 0.70 0.94 0.59 0.84 -0.52 0.63 0.43 1.00 NA NA NA
Ag 0.51 -0.14 -0.18 -0.12 0.32 -0.07 -0.08 0.10 1.00 NA NA
Cd 0.31 0.92 0.80 0.89 -0.81 0.82 0.60 0.76 -0.21 1.00 NA
Sn 0.54 0.90 0.91 0.96 -0.55 0.87 0.80 0.80 -0.10 0.90 1.00
Sb 0.41 0.85 0.97 0.97 -0.62 0.93 0.85 0.73 -0.16 0.91 0.96
Cs 0.31 0.63 0.99 0.87 -0.39 0.91 0.95 0.51 -0.17 0.74 0.87
Ba 0.46 0.85 0.95 0.98 -0.59 0.90 0.84 0.74 -0.19 0.85 0.94
La 0.22 -0.42 0.06 -0.16 0.84 -0.04 0.28 -0.28 0.30 -0.47 -0.10
Ce 0.26 -0.14 0.44 0.17 0.54 0.36 0.60 -0.10 0.16 -0.07 0.25
Pr 0.16 -0.11 0.51 0.21 0.48 0.38 0.66 -0.11 0.07 -0.01 0.31
Nd 0.20 -0.06 0.56 0.27 0.37 0.49 0.71 -0.08 0.02 0.07 0.34
Sm 0.01 -0.66 -0.26 -0.47 0.89 -0.36 -0.02 -0.51 0.17 -0.70 -0.40
Eu 0.01 -0.55 -0.04 -0.31 0.86 -0.10 0.17 -0.45 0.11 -0.54 -0.24
Gd 0.17 -0.51 -0.11 -0.32 0.90 -0.13 0.12 -0.35 0.37 -0.54 -0.23
Tb -0.08 -0.73 -0.53 -0.67 0.98 -0.55 -0.34 -0.55 0.29 -0.82 -0.60
Dy -0.05 -0.78 -0.64 -0.73 0.97 -0.65 -0.42 -0.56 0.37 -0.91 -0.69
Ho -0.09 -0.79 -0.64 -0.75 0.96 -0.65 -0.44 -0.57 0.41 -0.90 -0.71
Er -0.08 -0.76 -0.57 -0.70 0.99 -0.59 -0.36 -0.55 0.32 -0.88 -0.66
Tm -0.12 -0.73 -0.57 -0.70 0.97 -0.59 -0.40 -0.54 0.28 -0.83 -0.64
Yb -0.06 -0.67 -0.20 -0.46 0.90 -0.30 0.05 -0.51 0.20 -0.69 -0.40
Lu 0.21 -0.34 0.20 -0.06 0.73 0.14 0.43 -0.24 0.18 -0.35 0.01
Hf 0.47 0.74 0.93 0.90 -0.49 1.00 0.87 0.64 -0.07 0.83 0.88
Ta 0.44 0.67 0.96 0.88 -0.38 0.92 0.95 0.59 -0.17 0.74 0.88
W 0.64 0.94 0.87 0.99 -0.57 0.87 0.75 0.89 -0.05 0.88 0.97
Tl 0.51 0.84 0.96 0.97 -0.54 0.93 0.88 0.73 -0.16 0.86 0.97
Pb 0.37 0.82 0.96 0.94 -0.62 0.94 0.85 0.68 -0.22 0.92 0.95
Bi 0.37 0.82 0.97 0.94 -0.61 0.94 0.86 0.67 -0.20 0.91 0.96
Th 0.14 0.00 0.65 0.35 0.27 0.53 0.82 -0.03 0.05 0.11 0.38
U 0.27 -0.30 0.06 -0.07 0.67 -0.03 0.29 -0.11 0.49 -0.42 -0.10
Sb Cs Ba La Ce Pr Nd Sm Eu Gd Tb Dy
depth NA NA NA NA NA NA NA NA NA NA NA NA
Li NA NA NA NA NA NA NA NA NA NA NA NA
Be NA NA NA NA NA NA NA NA NA NA NA NA
P NA NA NA NA NA NA NA NA NA NA NA NA
Sc NA NA NA NA NA NA NA NA NA NA NA NA
Ti NA NA NA NA NA NA NA NA NA NA NA NA
V NA NA NA NA NA NA NA NA NA NA NA NA
Cr NA NA NA NA NA NA NA NA NA NA NA NA
Mn NA NA NA NA NA NA NA NA NA NA NA NA
Co NA NA NA NA NA NA NA NA NA NA NA NA
Ni NA NA NA NA NA NA NA NA NA NA NA NA
Cu NA NA NA NA NA NA NA NA NA NA NA NA
Zn NA NA NA NA NA NA NA NA NA NA NA NA
Rb NA NA NA NA NA NA NA NA NA NA NA NA
Sr NA NA NA NA NA NA NA NA NA NA NA NA
Y NA NA NA NA NA NA NA NA NA NA NA NA
Zr NA NA NA NA NA NA NA NA NA NA NA NA
Nb NA NA NA NA NA NA NA NA NA NA NA NA
Mo NA NA NA NA NA NA NA NA NA NA NA NA
Ag NA NA NA NA NA NA NA NA NA NA NA NA
Cd NA NA NA NA NA NA NA NA NA NA NA NA
Sn NA NA NA NA NA NA NA NA NA NA NA NA
Sb 1.00 NA NA NA NA NA NA NA NA NA NA NA
Cs 0.94 1.00 NA NA NA NA NA NA NA NA NA NA
Ba 0.97 0.91 1.00 NA NA NA NA NA NA NA NA NA
La -0.14 0.13 -0.11 1.00 NA NA NA NA NA NA NA NA
Ce 0.25 0.52 0.24 0.88 1.00 NA NA NA NA NA NA NA
Pr 0.31 0.58 0.29 0.84 0.98 1.00 NA NA NA NA NA NA
Nd 0.37 0.64 0.35 0.75 0.97 0.97 1.00 NA NA NA NA NA
Sm -0.44 -0.18 -0.42 0.86 0.67 0.62 0.56 1.00 NA NA NA NA
Eu -0.25 0.04 -0.24 0.94 0.85 0.81 0.76 0.91 1.00 NA NA NA
Gd -0.28 -0.03 -0.30 0.95 0.82 0.75 0.69 0.90 0.95 1.00 NA NA
Tb -0.67 -0.46 -0.64 0.78 0.48 0.41 0.31 0.86 0.83 0.85 1.00 NA
Dy -0.76 -0.58 -0.72 0.72 0.34 0.26 0.15 0.82 0.73 0.78 0.97 1.00
Ho -0.77 -0.59 -0.73 0.70 0.33 0.25 0.13 0.78 0.71 0.77 0.96 0.99
Er -0.71 -0.51 -0.68 0.76 0.41 0.34 0.23 0.84 0.78 0.82 0.98 0.99
Tm -0.70 -0.50 -0.68 0.72 0.41 0.35 0.24 0.83 0.77 0.80 0.99 0.96
Yb -0.41 -0.12 -0.40 0.87 0.68 0.66 0.58 0.94 0.90 0.89 0.84 0.82
Lu 0.00 0.27 0.01 0.91 0.88 0.86 0.81 0.85 0.91 0.88 0.66 0.58
Hf 0.93 0.92 0.91 -0.03 0.36 0.39 0.49 -0.35 -0.10 -0.13 -0.55 -0.65
Ta 0.92 0.96 0.91 0.10 0.46 0.51 0.59 -0.16 0.02 -0.05 -0.46 -0.56
W 0.94 0.82 0.95 -0.14 0.17 0.20 0.25 -0.44 -0.30 -0.27 -0.62 -0.68
Tl 0.98 0.93 0.98 -0.05 0.32 0.37 0.44 -0.35 -0.17 -0.21 -0.60 -0.69
Pb 0.99 0.94 0.94 -0.16 0.27 0.33 0.42 -0.42 -0.22 -0.27 -0.66 -0.78
Bi 0.99 0.95 0.95 -0.14 0.27 0.34 0.42 -0.42 -0.22 -0.26 -0.66 -0.77
Th 0.45 0.71 0.44 0.70 0.87 0.91 0.89 0.41 0.62 0.55 0.19 0.09
U -0.09 0.11 -0.05 0.83 0.64 0.60 0.49 0.61 0.67 0.74 0.60 0.63
Ho Er Tm Yb Lu Hf Ta W Tl Pb Bi
depth NA NA NA NA NA NA NA NA NA NA NA
Li NA NA NA NA NA NA NA NA NA NA NA
Be NA NA NA NA NA NA NA NA NA NA NA
P NA NA NA NA NA NA NA NA NA NA NA
Sc NA NA NA NA NA NA NA NA NA NA NA
Ti NA NA NA NA NA NA NA NA NA NA NA
V NA NA NA NA NA NA NA NA NA NA NA
Cr NA NA NA NA NA NA NA NA NA NA NA
Mn NA NA NA NA NA NA NA NA NA NA NA
Co NA NA NA NA NA NA NA NA NA NA NA
Ni NA NA NA NA NA NA NA NA NA NA NA
Cu NA NA NA NA NA NA NA NA NA NA NA
Zn NA NA NA NA NA NA NA NA NA NA NA
Rb NA NA NA NA NA NA NA NA NA NA NA
Sr NA NA NA NA NA NA NA NA NA NA NA
Y NA NA NA NA NA NA NA NA NA NA NA
Zr NA NA NA NA NA NA NA NA NA NA NA
Nb NA NA NA NA NA NA NA NA NA NA NA
Mo NA NA NA NA NA NA NA NA NA NA NA
Ag NA NA NA NA NA NA NA NA NA NA NA
Cd NA NA NA NA NA NA NA NA NA NA NA
Sn NA NA NA NA NA NA NA NA NA NA NA
Sb NA NA NA NA NA NA NA NA NA NA NA
Cs NA NA NA NA NA NA NA NA NA NA NA
Ba NA NA NA NA NA NA NA NA NA NA NA
La NA NA NA NA NA NA NA NA NA NA NA
Ce NA NA NA NA NA NA NA NA NA NA NA
Pr NA NA NA NA NA NA NA NA NA NA NA
Nd NA NA NA NA NA NA NA NA NA NA NA
Sm NA NA NA NA NA NA NA NA NA NA NA
Eu NA NA NA NA NA NA NA NA NA NA NA
Gd NA NA NA NA NA NA NA NA NA NA NA
Tb NA NA NA NA NA NA NA NA NA NA NA
Dy NA NA NA NA NA NA NA NA NA NA NA
Ho 1.00 NA NA NA NA NA NA NA NA NA NA
Er 0.98 1.00 NA NA NA NA NA NA NA NA NA
Tm 0.95 0.98 1.00 NA NA NA NA NA NA NA NA
Yb 0.79 0.87 0.83 1.00 NA NA NA NA NA NA NA
Lu 0.55 0.63 0.61 0.84 1.00 NA NA NA NA NA NA
Hf -0.65 -0.59 -0.60 -0.29 0.14 1.00 NA NA NA NA NA
Ta -0.59 -0.49 -0.49 -0.11 0.29 0.93 1.00 NA NA NA NA
W -0.70 -0.65 -0.64 -0.44 -0.04 0.88 0.86 1.00 NA NA NA
Tl -0.71 -0.65 -0.64 -0.35 0.09 0.93 0.94 0.96 1.00 NA NA
Pb -0.79 -0.72 -0.69 -0.40 0.01 0.94 0.93 0.92 0.97 1.00 NA
Bi -0.77 -0.71 -0.70 -0.39 0.03 0.95 0.93 0.92 0.98 1.00 1.00
Th 0.09 0.17 0.12 0.52 0.75 0.53 0.65 0.30 0.49 0.45 0.47
U 0.64 0.64 0.54 0.70 0.70 -0.02 0.07 -0.08 -0.04 -0.17 -0.13
Th U
depth NA NA
Li NA NA
Be NA NA
P NA NA
Sc NA NA
Ti NA NA
V NA NA
Cr NA NA
Mn NA NA
Co NA NA
Ni NA NA
Cu NA NA
Zn NA NA
Rb NA NA
Sr NA NA
Y NA NA
Zr NA NA
Nb NA NA
Mo NA NA
Ag NA NA
Cd NA NA
Sn NA NA
Sb NA NA
Cs NA NA
Ba NA NA
La NA NA
Ce NA NA
Pr NA NA
Nd NA NA
Sm NA NA
Eu NA NA
Gd NA NA
Tb NA NA
Dy NA NA
Ho NA NA
Er NA NA
Tm NA NA
Yb NA NA
Lu NA NA
Hf NA NA
Ta NA NA
W NA NA
Tl NA NA
Pb NA NA
Bi NA NA
Th 1.00 NA
U 0.65 1Показываем только больше 0,5
Scree plot
Сколько факторов выбрать?
The determinant of the smoothed correlation was zero.
This means the objective function is not defined for the null model either.
The Chi square is thus based upon observed correlations.In factor.scores, the correlation matrix is singular, an approximation is used
Factor analysis
Проведём анализ с 3 факторами.
The determinant of the smoothed correlation was zero.
This means the objective function is not defined for the null model either.
The Chi square is thus based upon observed correlations.In factor.scores, the correlation matrix is singular, an approximation is usedFactor Analysis using method = minres
Call: fa(r = lake3, nfactors = 3)
Warning: A Heywood case was detected.
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR2 MR3 h2 u2 com
depth -0.81 0.45 -0.08 0.99 0.0059 1.6
Li 1.00 0.16 -0.05 0.98 0.0184 1.1
Be 0.34 0.77 0.46 0.72 0.2824 2.1
P -0.05 -0.16 0.93 0.97 0.0330 1.1
Sc -0.71 0.50 -0.16 0.94 0.0589 1.9
Ti 0.96 0.24 -0.01 0.92 0.0841 1.1
V 0.63 -0.11 0.57 0.93 0.0708 2.0
Cr 0.99 0.14 0.03 0.97 0.0260 1.0
Mn 0.86 -0.33 0.01 0.93 0.0738 1.3
Co 0.75 0.06 0.52 0.96 0.0388 1.8
Ni 0.85 -0.09 0.32 0.97 0.0321 1.3
Cu 0.34 0.42 0.73 0.72 0.2822 2.1
Zn 0.65 -0.29 0.48 0.97 0.0311 2.3
Rb 1.01 0.03 -0.08 0.99 0.0116 1.0
Sr 0.88 -0.10 0.26 0.99 0.0142 1.2
Y -0.41 0.87 0.03 0.99 0.0082 1.4
Zr 0.94 0.00 0.04 0.89 0.1078 1.0
Nb 0.98 0.25 -0.14 0.95 0.0498 1.2
Mo 0.50 -0.05 0.74 0.98 0.0232 1.8
Ag -0.20 0.45 0.48 0.33 0.6665 2.3
Cd 0.76 -0.43 0.15 0.94 0.0596 1.7
Sn 0.89 -0.04 0.24 0.96 0.0442 1.2
Sb 0.95 -0.13 0.07 0.99 0.0111 1.0
Cs 1.02 0.08 -0.16 0.99 0.0126 1.1
Ba 0.93 -0.09 0.12 0.96 0.0448 1.1
La 0.12 0.99 -0.03 0.98 0.0191 1.0
Ce 0.52 0.83 -0.20 0.95 0.0474 1.8
Pr 0.59 0.75 -0.29 0.96 0.0422 2.2
Nd 0.66 0.66 -0.35 0.94 0.0628 2.5
Sm -0.17 0.81 -0.19 0.86 0.1381 1.2
Eu 0.05 0.88 -0.25 0.95 0.0498 1.2
Gd -0.04 0.96 -0.01 0.95 0.0522 1.0
Tb -0.48 0.81 0.03 0.96 0.0400 1.6
Dy -0.61 0.76 0.10 1.00 0.0032 1.9
Ho -0.62 0.74 0.10 0.99 0.0074 2.0
Er -0.54 0.80 0.05 0.99 0.0135 1.8
Tm -0.53 0.76 0.04 0.93 0.0686 1.8
Yb -0.13 0.84 -0.22 0.91 0.0911 1.2
Lu 0.28 0.90 -0.17 0.92 0.0789 1.3
Hf 0.94 0.01 0.05 0.90 0.0958 1.0
Ta 0.99 0.11 -0.05 0.95 0.0532 1.0
W 0.84 -0.04 0.39 1.00 0.0037 1.4
Tl 0.96 -0.03 0.11 0.99 0.0098 1.0
Pb 0.97 -0.15 -0.01 0.98 0.0163 1.1
Bi 0.97 -0.14 -0.01 0.99 0.0111 1.0
Th 0.71 0.61 -0.33 0.90 0.0959 2.4
U 0.07 0.86 0.17 0.68 0.3169 1.1
MR1 MR2 MR3
SS loadings 24.62 13.97 5.00
Proportion Var 0.52 0.30 0.11
Cumulative Var 0.52 0.82 0.93
Proportion Explained 0.56 0.32 0.11
Cumulative Proportion 0.56 0.89 1.00
With factor correlations of
MR1 MR2 MR3
MR1 1.00 -0.11 0.20
MR2 -0.11 1.00 -0.28
MR3 0.20 -0.28 1.00
Mean item complexity = 1.5
Test of the hypothesis that 3 factors are sufficient.
The degrees of freedom for the null model are 1081 and the objective function was 932.78 with Chi Square of -4197.52
The degrees of freedom for the model are 943 and the objective function was 676.21
The root mean square of the residuals (RMSR) is 0.02
The df corrected root mean square of the residuals is 0.02
The harmonic number of observations is 13 with the empirical chi square 15.13 with prob < 1
The total number of observations was 13 with Likelihood Chi Square = 0 with prob < 1
Tucker Lewis Index of factoring reliability = 0.143
RMSEA index = 0.796 and the 90 % confidence intervals are 0 NA
BIC = -6814.12
Fit based upon off diagonal values = 1Каждый объединяет хим элементы следующим образом:
Loadings:
MR1 MR2 MR3
depth -0.814 0.448
Li 1.003 0.156
Be 0.340 0.766 0.458
P -0.164 0.934
Sc -0.706 0.499 -0.160
Ti 0.955 0.236
V 0.633 -0.107 0.571
Cr 0.987 0.145
Mn 0.864 -0.334
Co 0.751 0.518
Ni 0.849 0.316
Cu 0.339 0.425 0.729
Zn 0.646 -0.288 0.478
Rb 1.010
Sr 0.884 -0.102 0.261
Y -0.414 0.871
Zr 0.935
Nb 0.979 0.245 -0.143
Mo 0.502 0.740
Ag -0.201 0.447 0.482
Cd 0.762 -0.428 0.148
Sn 0.892 0.243
Sb 0.953 -0.126
Cs 1.015 -0.160
Ba 0.929 0.117
La 0.120 0.987
Ce 0.525 0.828 -0.197
Pr 0.590 0.754 -0.293
Nd 0.662 0.660 -0.351
Sm -0.172 0.813 -0.194
Eu 0.880 -0.253
Gd 0.965
Tb -0.483 0.809
Dy -0.607 0.762
Ho -0.624 0.744
Er -0.536 0.796
Tm -0.534 0.759
Yb -0.134 0.837 -0.223
Lu 0.283 0.896 -0.170
Hf 0.941
Ta 0.986 0.106
W 0.838 0.388
Tl 0.964 0.107
Pb 0.965 -0.154
Bi 0.971 -0.139
Th 0.710 0.607 -0.330
U 0.860 0.167
MR1 MR2 MR3
SS loadings 24.054 13.508 4.330
Proportion Var 0.512 0.287 0.092
Cumulative Var 0.512 0.799 0.8911 фактор описывает данные на 51.2%
1+2 факторы описывают данные на 79.9%
1+2+3 факторы описывают данные на 89.1% 
3D репрезентация исходных наблюдений в новом пространстве факторов.
All lakes together
Describe data
Опишем имеющиеся данные:| vars | n | mean | sd | median | trimmed | mad | min | max | range | skew | kurtosis | se | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| depth | 1 | 51 | 17.53 | 11.81 | 15.00 | 16.44 | 11.86 | 1.00 | 47.00 | 46.00 | 0.70 | -0.32 | 1.65 |
| Li | 2 | 51 | 10.55 | 12.55 | 4.05 | 8.28 | 4.44 | 0.34 | 46.67 | 46.33 | 1.40 | 0.84 | 1.76 |
| Be | 3 | 51 | 0.68 | 0.40 | 0.59 | 0.62 | 0.35 | 0.26 | 1.84 | 1.59 | 1.02 | 0.21 | 0.06 |
| P | 4 | 51 | 9641.16 | 11562.99 | 2445.00 | 7711.15 | 1925.90 | 1058.00 | 37830.00 | 36772.00 | 1.09 | -0.32 | 1619.14 |
| Sc | 5 | 51 | 9.99 | 4.84 | 8.87 | 9.88 | 6.33 | 2.71 | 19.49 | 16.78 | 0.16 | -1.37 | 0.68 |
| Ti | 6 | 51 | 1159.61 | 1149.56 | 582.00 | 965.01 | 442.26 | 113.70 | 4284.00 | 4170.30 | 1.31 | 0.49 | 160.97 |
| V | 7 | 51 | 396.56 | 927.18 | 43.16 | 151.62 | 40.06 | 13.65 | 4785.00 | 4771.35 | 3.34 | 11.37 | 129.83 |
| Cr | 8 | 51 | 48.86 | 45.03 | 31.67 | 40.78 | 27.04 | 10.14 | 195.80 | 185.66 | 1.48 | 1.54 | 6.31 |
| Mn | 9 | 51 | 1346.87 | 1267.76 | 918.20 | 1170.27 | 1230.23 | 65.38 | 4400.00 | 4334.62 | 0.95 | -0.16 | 177.52 |
| Co | 10 | 51 | 13.22 | 7.68 | 14.57 | 13.19 | 7.49 | 1.81 | 26.00 | 24.19 | -0.27 | -1.20 | 1.08 |
| Ni | 11 | 51 | 91.65 | 137.73 | 38.07 | 56.41 | 34.74 | 9.67 | 606.50 | 596.83 | 2.51 | 5.73 | 19.29 |
| Cu | 12 | 51 | 229.29 | 292.72 | 111.10 | 165.73 | 115.35 | 23.64 | 1260.00 | 1236.36 | 1.83 | 2.62 | 40.99 |
| Zn | 13 | 51 | 320.22 | 201.66 | 311.10 | 307.49 | 223.87 | 39.96 | 962.60 | 922.64 | 0.57 | 0.25 | 28.24 |
| Rb | 14 | 51 | 25.86 | 29.30 | 10.62 | 20.39 | 8.74 | 1.35 | 103.90 | 102.55 | 1.38 | 0.63 | 4.10 |
| Sr | 15 | 51 | 61.70 | 26.41 | 61.23 | 59.82 | 29.09 | 26.31 | 118.80 | 92.49 | 0.42 | -0.86 | 3.70 |
| Y | 16 | 51 | 8.83 | 3.88 | 7.65 | 8.25 | 2.51 | 3.98 | 20.25 | 16.27 | 1.33 | 1.11 | 0.54 |
| Zr | 17 | 51 | 45.48 | 31.39 | 35.94 | 42.69 | 30.20 | 6.36 | 114.10 | 107.74 | 0.64 | -0.94 | 4.39 |
| Nb | 18 | 51 | 2.52 | 2.46 | 1.41 | 2.10 | 1.31 | 0.23 | 9.75 | 9.52 | 1.43 | 1.02 | 0.34 |
| Mo | 19 | 51 | 2.95 | 2.26 | 2.68 | 2.63 | 2.07 | 0.71 | 13.32 | 12.61 | 2.04 | 6.47 | 0.32 |
| Ag | 20 | 51 | 0.60 | 0.28 | 0.52 | 0.58 | 0.22 | 0.22 | 1.68 | 1.47 | 1.38 | 2.91 | 0.04 |
| Cd | 21 | 51 | 0.74 | 0.27 | 0.72 | 0.73 | 0.32 | 0.22 | 1.32 | 1.10 | 0.25 | -0.75 | 0.04 |
| Sn | 22 | 51 | 6.26 | 5.88 | 3.80 | 5.46 | 3.44 | 0.38 | 22.16 | 21.78 | 1.11 | 0.11 | 0.82 |
| Sb | 23 | 51 | 1.15 | 0.89 | 1.12 | 1.05 | 0.99 | 0.10 | 3.90 | 3.80 | 0.99 | 0.72 | 0.12 |
| Cs | 24 | 51 | 1.14 | 1.21 | 0.60 | 0.92 | 0.62 | 0.05 | 4.52 | 4.47 | 1.41 | 0.78 | 0.17 |
| Ba | 25 | 51 | 554.68 | 560.53 | 390.10 | 450.15 | 409.20 | 77.95 | 2249.00 | 2171.05 | 1.47 | 1.48 | 78.49 |
| La | 26 | 51 | 16.14 | 7.75 | 15.75 | 15.08 | 7.07 | 7.10 | 37.10 | 30.00 | 1.05 | 0.44 | 1.08 |
| Ce | 27 | 51 | 32.39 | 14.15 | 31.25 | 31.19 | 12.30 | 13.49 | 63.16 | 49.67 | 0.47 | -0.64 | 1.98 |
| Pr | 28 | 51 | 3.91 | 1.92 | 3.80 | 3.67 | 1.54 | 1.54 | 9.22 | 7.68 | 0.97 | 0.38 | 0.27 |
| Nd | 29 | 51 | 14.55 | 7.26 | 13.99 | 13.60 | 5.35 | 5.93 | 34.07 | 28.13 | 0.99 | 0.40 | 1.02 |
| Sm | 30 | 51 | 2.78 | 1.32 | 2.55 | 2.59 | 1.04 | 1.16 | 6.48 | 5.33 | 1.16 | 0.75 | 0.19 |
| Eu | 31 | 51 | 0.60 | 0.27 | 0.58 | 0.56 | 0.23 | 0.25 | 1.38 | 1.13 | 1.12 | 0.83 | 0.04 |
| Gd | 32 | 51 | 2.23 | 1.06 | 1.97 | 2.07 | 0.80 | 0.97 | 5.30 | 4.33 | 1.26 | 0.86 | 0.15 |
| Tb | 33 | 51 | 0.32 | 0.13 | 0.28 | 0.30 | 0.09 | 0.16 | 0.71 | 0.56 | 1.39 | 1.34 | 0.02 |
| Dy | 34 | 51 | 1.77 | 0.78 | 1.54 | 1.64 | 0.44 | 0.82 | 4.14 | 3.32 | 1.46 | 1.44 | 0.11 |
| Ho | 35 | 51 | 0.34 | 0.15 | 0.32 | 0.32 | 0.10 | 0.16 | 0.80 | 0.64 | 1.46 | 1.48 | 0.02 |
| Er | 36 | 51 | 0.98 | 0.46 | 0.87 | 0.89 | 0.24 | 0.45 | 2.38 | 1.93 | 1.55 | 1.67 | 0.06 |
| Tm | 37 | 51 | 0.13 | 0.07 | 0.11 | 0.12 | 0.04 | 0.06 | 0.33 | 0.26 | 1.40 | 1.02 | 0.01 |
| Yb | 38 | 51 | 0.85 | 0.44 | 0.69 | 0.77 | 0.26 | 0.39 | 2.13 | 1.74 | 1.44 | 1.10 | 0.06 |
| Lu | 39 | 51 | 0.12 | 0.07 | 0.10 | 0.11 | 0.04 | 0.05 | 0.33 | 0.27 | 1.64 | 2.05 | 0.01 |
| Hf | 40 | 51 | 1.21 | 0.88 | 0.85 | 1.09 | 0.68 | 0.18 | 3.52 | 3.34 | 0.94 | -0.12 | 0.12 |
| Ta | 41 | 51 | 0.24 | 0.26 | 0.10 | 0.19 | 0.09 | 0.02 | 1.05 | 1.03 | 1.45 | 1.31 | 0.04 |
| W | 42 | 51 | 1.09 | 0.88 | 0.92 | 0.97 | 0.88 | 0.15 | 4.37 | 4.22 | 1.39 | 2.36 | 0.12 |
| Tl | 43 | 51 | 0.30 | 0.20 | 0.24 | 0.28 | 0.20 | 0.05 | 0.80 | 0.74 | 0.79 | -0.36 | 0.03 |
| Pb | 44 | 51 | 45.41 | 26.78 | 44.29 | 43.31 | 21.90 | 3.19 | 137.07 | 133.88 | 0.85 | 1.36 | 3.75 |
| Bi | 45 | 51 | 0.25 | 0.16 | 0.24 | 0.23 | 0.10 | 0.04 | 0.98 | 0.94 | 2.09 | 7.05 | 0.02 |
| Th | 46 | 51 | 3.51 | 3.02 | 2.01 | 2.95 | 1.13 | 0.90 | 12.09 | 11.19 | 1.48 | 0.97 | 0.42 |
| U | 47 | 51 | 1.28 | 1.11 | 0.60 | 1.09 | 0.38 | 0.28 | 3.92 | 3.64 | 1.17 | 0.09 | 0.16 |
Матрица корреляций.
depth Li Be P Sc Ti V Cr Mn Co Ni
depth 1.00 NA NA NA NA NA NA NA NA NA NA
Li -0.52 1.00 NA NA NA NA NA NA NA NA NA
Be -0.47 0.96 1.00 NA NA NA NA NA NA NA NA
P 0.73 -0.36 -0.25 1.00 NA NA NA NA NA NA NA
Sc -0.55 0.44 0.31 -0.59 1.00 NA NA NA NA NA NA
Ti -0.57 0.99 0.94 -0.38 0.46 1.00 NA NA NA NA NA
V -0.28 0.40 0.41 -0.05 0.04 0.43 1.00 NA NA NA NA
Cr -0.44 0.88 0.84 -0.28 0.29 0.86 0.57 1.00 NA NA NA
Mn 0.66 -0.17 -0.06 0.96 -0.58 -0.20 -0.05 -0.13 1.00 NA NA
Co -0.03 0.64 0.76 0.32 -0.18 0.61 0.36 0.59 0.51 1.00 NA
Ni -0.33 0.47 0.49 -0.07 0.00 0.50 0.97 0.60 -0.05 0.43 1.00
Cu -0.37 0.29 0.36 0.02 -0.13 0.33 0.59 0.34 0.09 0.41 0.68
Zn -0.10 0.28 0.39 0.40 -0.39 0.28 0.57 0.42 0.48 0.66 0.67
Rb -0.53 0.99 0.95 -0.34 0.44 1.00 0.46 0.88 -0.17 0.64 0.52
Sr -0.29 0.81 0.86 0.11 0.02 0.81 0.39 0.70 0.31 0.88 0.48
Y -0.42 0.94 0.94 -0.28 0.37 0.92 0.25 0.84 -0.06 0.69 0.32
Zr -0.67 0.81 0.79 -0.32 0.46 0.83 0.35 0.70 -0.20 0.47 0.38
Nb -0.57 0.99 0.94 -0.41 0.51 0.99 0.38 0.87 -0.23 0.57 0.45
Mo -0.02 0.16 0.27 0.39 -0.32 0.17 0.66 0.32 0.42 0.54 0.73
Ag 0.38 -0.28 -0.15 0.41 -0.41 -0.31 -0.32 -0.28 0.42 0.20 -0.27
Cd -0.50 0.00 0.05 -0.29 -0.13 -0.02 0.04 0.10 -0.27 -0.02 0.08
Sn -0.18 0.13 0.25 0.27 -0.24 0.14 0.47 0.25 0.31 0.49 0.51
Sb -0.34 0.25 0.38 -0.19 -0.03 0.21 -0.04 0.33 -0.08 0.41 0.02
Cs -0.56 0.99 0.93 -0.39 0.50 0.99 0.42 0.89 -0.22 0.58 0.48
Ba 0.60 -0.15 -0.04 0.91 -0.49 -0.17 -0.04 -0.12 0.94 0.49 -0.05
La -0.31 0.92 0.94 -0.10 0.21 0.89 0.30 0.85 0.12 0.80 0.37
Ce -0.20 0.84 0.90 0.11 0.02 0.83 0.41 0.80 0.30 0.90 0.48
Pr -0.30 0.91 0.93 -0.09 0.20 0.88 0.29 0.84 0.13 0.82 0.37
Nd -0.31 0.91 0.92 -0.11 0.19 0.88 0.27 0.85 0.11 0.80 0.35
Sm -0.32 0.92 0.92 -0.17 0.24 0.88 0.24 0.84 0.05 0.76 0.31
Eu -0.29 0.91 0.92 -0.11 0.22 0.87 0.24 0.82 0.11 0.79 0.31
Gd -0.36 0.93 0.92 -0.22 0.27 0.90 0.25 0.85 0.00 0.72 0.32
Tb -0.42 0.95 0.93 -0.31 0.41 0.93 0.28 0.85 -0.11 0.66 0.35
Dy -0.41 0.93 0.90 -0.35 0.46 0.91 0.22 0.84 -0.15 0.59 0.28
Ho -0.42 0.92 0.89 -0.36 0.47 0.90 0.20 0.81 -0.16 0.58 0.26
Er -0.43 0.94 0.90 -0.37 0.48 0.92 0.22 0.83 -0.16 0.58 0.28
Tm -0.45 0.95 0.93 -0.34 0.40 0.93 0.24 0.84 -0.12 0.64 0.31
Yb -0.47 0.97 0.94 -0.33 0.41 0.95 0.28 0.86 -0.12 0.65 0.35
Lu -0.46 0.97 0.94 -0.33 0.43 0.95 0.25 0.84 -0.12 0.65 0.32
Hf -0.66 0.91 0.87 -0.39 0.50 0.92 0.35 0.79 -0.24 0.50 0.40
Ta -0.48 0.92 0.91 -0.24 0.31 0.94 0.64 0.88 -0.09 0.68 0.69
W -0.57 0.51 0.60 -0.20 -0.03 0.53 0.30 0.47 -0.07 0.47 0.41
Tl -0.47 0.94 0.96 -0.24 0.23 0.93 0.45 0.90 -0.05 0.77 0.53
Pb -0.14 0.10 0.22 0.17 -0.15 0.06 -0.12 0.16 0.24 0.44 -0.09
Bi -0.13 0.20 0.33 0.14 -0.14 0.18 0.00 0.24 0.19 0.48 0.04
Th -0.52 0.99 0.94 -0.38 0.47 0.98 0.38 0.91 -0.20 0.60 0.44
U -0.55 0.94 0.91 -0.40 0.39 0.93 0.40 0.87 -0.19 0.60 0.47
Cu Zn Rb Sr Y Zr Nb Mo Ag Cd Sn Sb
depth NA NA NA NA NA NA NA NA NA NA NA NA
Li NA NA NA NA NA NA NA NA NA NA NA NA
Be NA NA NA NA NA NA NA NA NA NA NA NA
P NA NA NA NA NA NA NA NA NA NA NA NA
Sc NA NA NA NA NA NA NA NA NA NA NA NA
Ti NA NA NA NA NA NA NA NA NA NA NA NA
V NA NA NA NA NA NA NA NA NA NA NA NA
Cr NA NA NA NA NA NA NA NA NA NA NA NA
Mn NA NA NA NA NA NA NA NA NA NA NA NA
Co NA NA NA NA NA NA NA NA NA NA NA NA
Ni NA NA NA NA NA NA NA NA NA NA NA NA
Cu 1.00 NA NA NA NA NA NA NA NA NA NA NA
Zn 0.79 1.00 NA NA NA NA NA NA NA NA NA NA
Rb 0.32 0.29 1.00 NA NA NA NA NA NA NA NA NA
Sr 0.45 0.60 0.82 1.00 NA NA NA NA NA NA NA NA
Y 0.24 0.27 0.92 0.81 1.00 NA NA NA NA NA NA NA
Zr 0.25 0.23 0.83 0.66 0.72 1.00 NA NA NA NA NA NA
Nb 0.25 0.22 0.99 0.76 0.93 0.85 1.00 NA NA NA NA NA
Mo 0.78 0.91 0.18 0.42 0.13 0.13 0.11 1.00 NA NA NA NA
Ag -0.19 0.07 -0.30 0.04 -0.13 -0.31 -0.31 0.04 1.00 NA NA NA
Cd 0.08 0.16 -0.02 -0.04 -0.01 0.26 0.01 0.08 -0.02 1.00 NA NA
Sn 0.76 0.74 0.15 0.41 0.12 0.13 0.08 0.76 0.16 0.09 1.00 NA
Sb 0.13 0.22 0.21 0.27 0.33 0.26 0.23 0.13 0.33 0.50 0.36 1.00
Cs 0.27 0.24 0.99 0.77 0.92 0.84 1.00 0.14 -0.32 0.01 0.10 0.22
Ba 0.05 0.43 -0.14 0.34 -0.05 -0.16 -0.20 0.36 0.46 -0.30 0.34 -0.11
La 0.29 0.40 0.91 0.89 0.97 0.69 0.89 0.24 -0.08 -0.01 0.21 0.35
Ce 0.41 0.56 0.85 0.96 0.88 0.65 0.81 0.40 -0.01 -0.08 0.36 0.29
Pr 0.29 0.41 0.90 0.88 0.96 0.68 0.88 0.25 -0.08 0.00 0.22 0.37
Nd 0.27 0.39 0.89 0.87 0.96 0.66 0.88 0.23 -0.08 0.01 0.20 0.38
Sm 0.23 0.33 0.89 0.83 0.98 0.65 0.89 0.17 -0.09 0.01 0.15 0.38
Eu 0.24 0.35 0.88 0.86 0.97 0.66 0.88 0.19 -0.07 -0.02 0.18 0.35
Gd 0.21 0.30 0.90 0.82 0.99 0.68 0.91 0.13 -0.10 0.03 0.12 0.36
Tb 0.23 0.24 0.93 0.78 0.99 0.71 0.94 0.12 -0.18 -0.03 0.10 0.30
Dy 0.15 0.16 0.90 0.72 0.99 0.67 0.92 0.04 -0.17 -0.04 0.03 0.31
Ho 0.15 0.15 0.90 0.71 0.98 0.68 0.92 0.03 -0.16 -0.03 0.02 0.30
Er 0.16 0.15 0.91 0.72 0.99 0.70 0.94 0.04 -0.19 -0.04 0.02 0.29
Tm 0.22 0.23 0.93 0.78 0.99 0.71 0.94 0.09 -0.17 0.00 0.09 0.32
Yb 0.23 0.24 0.95 0.80 0.99 0.75 0.96 0.11 -0.18 0.00 0.10 0.32
Lu 0.21 0.23 0.94 0.78 0.98 0.75 0.96 0.10 -0.18 0.01 0.09 0.32
Hf 0.24 0.21 0.92 0.71 0.82 0.97 0.94 0.11 -0.31 0.18 0.12 0.27
Ta 0.41 0.42 0.95 0.83 0.83 0.80 0.92 0.32 -0.30 -0.01 0.25 0.20
W 0.74 0.57 0.51 0.57 0.47 0.57 0.49 0.43 -0.21 0.31 0.49 0.39
Tl 0.35 0.44 0.93 0.85 0.91 0.80 0.92 0.31 -0.19 0.16 0.26 0.39
Pb 0.03 0.24 0.07 0.27 0.18 0.25 0.08 0.17 0.41 0.47 0.44 0.66
Bi 0.03 0.26 0.19 0.36 0.26 0.33 0.19 0.20 0.49 0.33 0.32 0.75
Th 0.24 0.24 0.98 0.77 0.95 0.80 0.99 0.12 -0.28 -0.01 0.09 0.25
U 0.34 0.32 0.93 0.75 0.94 0.72 0.93 0.20 -0.25 0.11 0.14 0.32
Cs Ba La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er
depth NA NA NA NA NA NA NA NA NA NA NA NA NA
Li NA NA NA NA NA NA NA NA NA NA NA NA NA
Be NA NA NA NA NA NA NA NA NA NA NA NA NA
P NA NA NA NA NA NA NA NA NA NA NA NA NA
Sc NA NA NA NA NA NA NA NA NA NA NA NA NA
Ti NA NA NA NA NA NA NA NA NA NA NA NA NA
V NA NA NA NA NA NA NA NA NA NA NA NA NA
Cr NA NA NA NA NA NA NA NA NA NA NA NA NA
Mn NA NA NA NA NA NA NA NA NA NA NA NA NA
Co NA NA NA NA NA NA NA NA NA NA NA NA NA
Ni NA NA NA NA NA NA NA NA NA NA NA NA NA
Cu NA NA NA NA NA NA NA NA NA NA NA NA NA
Zn NA NA NA NA NA NA NA NA NA NA NA NA NA
Rb NA NA NA NA NA NA NA NA NA NA NA NA NA
Sr NA NA NA NA NA NA NA NA NA NA NA NA NA
Y NA NA NA NA NA NA NA NA NA NA NA NA NA
Zr NA NA NA NA NA NA NA NA NA NA NA NA NA
Nb NA NA NA NA NA NA NA NA NA NA NA NA NA
Mo NA NA NA NA NA NA NA NA NA NA NA NA NA
Ag NA NA NA NA NA NA NA NA NA NA NA NA NA
Cd NA NA NA NA NA NA NA NA NA NA NA NA NA
Sn NA NA NA NA NA NA NA NA NA NA NA NA NA
Sb NA NA NA NA NA NA NA NA NA NA NA NA NA
Cs 1.00 NA NA NA NA NA NA NA NA NA NA NA NA
Ba -0.19 1.00 NA NA NA NA NA NA NA NA NA NA NA
La 0.89 0.11 1.00 NA NA NA NA NA NA NA NA NA NA
Ce 0.81 0.30 0.95 1.00 NA NA NA NA NA NA NA NA NA
Pr 0.88 0.11 1.00 0.95 1.00 NA NA NA NA NA NA NA NA
Nd 0.88 0.09 1.00 0.94 1.00 1.00 NA NA NA NA NA NA NA
Sm 0.88 0.05 0.99 0.91 0.99 1.00 1.00 NA NA NA NA NA NA
Eu 0.87 0.12 0.99 0.93 0.99 0.99 0.99 1.00 NA NA NA NA NA
Gd 0.90 -0.01 0.98 0.90 0.98 0.99 0.99 0.99 1.00 NA NA NA NA
Tb 0.93 -0.09 0.96 0.86 0.95 0.95 0.97 0.96 0.98 1.00 NA NA NA
Dy 0.91 -0.14 0.94 0.81 0.93 0.93 0.96 0.94 0.97 0.99 1.00 NA NA
Ho 0.91 -0.15 0.93 0.80 0.92 0.92 0.95 0.93 0.96 0.99 1.00 1.00 NA
Er 0.92 -0.15 0.93 0.80 0.92 0.93 0.95 0.94 0.97 0.99 1.00 1.00 1.00
Tm 0.93 -0.12 0.95 0.84 0.94 0.95 0.96 0.95 0.98 0.98 0.99 0.98 0.99
Yb 0.95 -0.11 0.96 0.86 0.95 0.96 0.97 0.96 0.98 0.99 0.98 0.98 0.99
Lu 0.95 -0.11 0.95 0.84 0.95 0.95 0.96 0.95 0.97 0.98 0.98 0.97 0.98
Hf 0.93 -0.20 0.79 0.72 0.78 0.77 0.77 0.77 0.79 0.82 0.79 0.79 0.81
Ta 0.93 -0.06 0.84 0.85 0.83 0.82 0.80 0.80 0.82 0.84 0.79 0.78 0.80
W 0.48 -0.12 0.48 0.53 0.49 0.48 0.45 0.45 0.45 0.43 0.39 0.39 0.40
Tl 0.92 -0.05 0.93 0.89 0.92 0.92 0.91 0.91 0.91 0.90 0.87 0.85 0.87
Pb 0.08 0.30 0.25 0.26 0.26 0.26 0.23 0.25 0.21 0.14 0.11 0.12 0.10
Bi 0.18 0.19 0.32 0.36 0.33 0.32 0.30 0.31 0.29 0.22 0.20 0.19 0.19
Th 0.99 -0.17 0.92 0.83 0.91 0.91 0.92 0.91 0.93 0.96 0.95 0.94 0.95
U 0.93 -0.21 0.91 0.80 0.90 0.91 0.92 0.90 0.93 0.93 0.94 0.93 0.94
Tm Yb Lu Hf Ta W Tl Pb Bi Th U
depth NA NA NA NA NA NA NA NA NA NA NA
Li NA NA NA NA NA NA NA NA NA NA NA
Be NA NA NA NA NA NA NA NA NA NA NA
P NA NA NA NA NA NA NA NA NA NA NA
Sc NA NA NA NA NA NA NA NA NA NA NA
Ti NA NA NA NA NA NA NA NA NA NA NA
V NA NA NA NA NA NA NA NA NA NA NA
Cr NA NA NA NA NA NA NA NA NA NA NA
Mn NA NA NA NA NA NA NA NA NA NA NA
Co NA NA NA NA NA NA NA NA NA NA NA
Ni NA NA NA NA NA NA NA NA NA NA NA
Cu NA NA NA NA NA NA NA NA NA NA NA
Zn NA NA NA NA NA NA NA NA NA NA NA
Rb NA NA NA NA NA NA NA NA NA NA NA
Sr NA NA NA NA NA NA NA NA NA NA NA
Y NA NA NA NA NA NA NA NA NA NA NA
Zr NA NA NA NA NA NA NA NA NA NA NA
Nb NA NA NA NA NA NA NA NA NA NA NA
Mo NA NA NA NA NA NA NA NA NA NA NA
Ag NA NA NA NA NA NA NA NA NA NA NA
Cd NA NA NA NA NA NA NA NA NA NA NA
Sn NA NA NA NA NA NA NA NA NA NA NA
Sb NA NA NA NA NA NA NA NA NA NA NA
Cs NA NA NA NA NA NA NA NA NA NA NA
Ba NA NA NA NA NA NA NA NA NA NA NA
La NA NA NA NA NA NA NA NA NA NA NA
Ce NA NA NA NA NA NA NA NA NA NA NA
Pr NA NA NA NA NA NA NA NA NA NA NA
Nd NA NA NA NA NA NA NA NA NA NA NA
Sm NA NA NA NA NA NA NA NA NA NA NA
Eu NA NA NA NA NA NA NA NA NA NA NA
Gd NA NA NA NA NA NA NA NA NA NA NA
Tb NA NA NA NA NA NA NA NA NA NA NA
Dy NA NA NA NA NA NA NA NA NA NA NA
Ho NA NA NA NA NA NA NA NA NA NA NA
Er NA NA NA NA NA NA NA NA NA NA NA
Tm 1.00 NA NA NA NA NA NA NA NA NA NA
Yb 0.99 1.00 NA NA NA NA NA NA NA NA NA
Lu 0.98 0.99 1.00 NA NA NA NA NA NA NA NA
Hf 0.83 0.86 0.86 1.00 NA NA NA NA NA NA NA
Ta 0.82 0.85 0.84 0.87 1.00 NA NA NA NA NA NA
W 0.47 0.48 0.45 0.55 0.53 1.00 NA NA NA NA NA
Tl 0.90 0.92 0.91 0.87 0.91 0.60 1.00 NA NA NA NA
Pb 0.14 0.15 0.17 0.20 0.07 0.17 0.27 1.00 NA NA NA
Bi 0.22 0.24 0.24 0.29 0.23 0.27 0.33 0.59 1.00 NA NA
Th 0.96 0.97 0.97 0.90 0.91 0.47 0.93 0.09 0.19 1.00 NA
U 0.95 0.96 0.95 0.83 0.85 0.52 0.90 0.09 0.16 0.94 1Показываем только больше 0,5
Scree plot
Сколько факторов выбрать?
Factor analysis
2 factors
Проведём анализ с 2 факторами.
Factor Analysis using method = minres
Call: fa(r = lakes, nfactors = 2)
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR2 h2 u2 com
depth -0.54 0.37 0.392 0.608 1.8
Li 0.99 -0.08 0.980 0.020 1.0
Be 0.96 0.10 0.952 0.048 1.0
P -0.38 0.79 0.717 0.283 1.4
Sc 0.43 -0.65 0.563 0.437 1.7
Ti 0.98 -0.10 0.960 0.040 1.0
V 0.37 0.26 0.215 0.785 1.8
Cr 0.89 0.05 0.802 0.198 1.0
Mn -0.18 0.83 0.693 0.307 1.1
Co 0.64 0.66 0.911 0.089 2.0
Ni 0.43 0.30 0.298 0.702 1.8
Cu 0.29 0.44 0.297 0.703 1.7
Zn 0.28 0.78 0.728 0.272 1.3
Rb 0.98 -0.07 0.958 0.042 1.0
Sr 0.80 0.44 0.890 0.110 1.5
Y 0.97 -0.01 0.948 0.052 1.0
Zr 0.80 -0.10 0.645 0.355 1.0
Nb 0.99 -0.16 0.977 0.023 1.1
Mo 0.16 0.72 0.564 0.436 1.1
Ag -0.25 0.40 0.207 0.793 1.7
Cd 0.06 -0.03 0.004 0.996 1.5
Sn 0.14 0.66 0.464 0.536 1.1
Sb 0.32 0.17 0.139 0.861 1.5
Cs 0.98 -0.14 0.967 0.033 1.0
Ba -0.16 0.78 0.617 0.383 1.1
La 0.94 0.18 0.952 0.048 1.1
Ce 0.85 0.42 0.958 0.042 1.5
Pr 0.94 0.19 0.944 0.056 1.1
Nd 0.94 0.17 0.932 0.068 1.1
Sm 0.94 0.10 0.915 0.085 1.0
Eu 0.93 0.15 0.913 0.087 1.1
Gd 0.96 0.05 0.925 0.075 1.0
Tb 0.97 -0.05 0.945 0.055 1.0
Dy 0.96 -0.13 0.922 0.078 1.0
Ho 0.96 -0.15 0.914 0.086 1.0
Er 0.97 -0.15 0.934 0.066 1.0
Tm 0.98 -0.08 0.949 0.051 1.0
Yb 0.99 -0.07 0.976 0.024 1.0
Lu 0.98 -0.08 0.962 0.038 1.0
Hf 0.90 -0.14 0.818 0.182 1.1
Ta 0.91 0.08 0.839 0.161 1.0
W 0.52 0.22 0.342 0.658 1.3
Tl 0.95 0.13 0.936 0.064 1.0
Pb 0.15 0.35 0.155 0.845 1.3
Bi 0.24 0.34 0.188 0.812 1.8
Th 0.99 -0.12 0.983 0.017 1.0
U 0.96 -0.08 0.925 0.075 1.0
MR1 MR2
SS loadings 28.14 6.08
Proportion Var 0.60 0.13
Cumulative Var 0.60 0.73
Proportion Explained 0.82 0.18
Cumulative Proportion 0.82 1.00
With factor correlations of
MR1 MR2
MR1 1.00 0.08
MR2 0.08 1.00
Mean item complexity = 1.2
Test of the hypothesis that 2 factors are sufficient.
The degrees of freedom for the null model are 1081 and the objective function was 206.5 with Chi Square of 6917.69
The degrees of freedom for the model are 988 and the objective function was 120.5
The root mean square of the residuals (RMSR) is 0.1
The df corrected root mean square of the residuals is 0.1
The harmonic number of observations is 51 with the empirical chi square 1092.13 with prob < 0.011
The total number of observations was 51 with Likelihood Chi Square = 3876.13 with prob < 0
Tucker Lewis Index of factoring reliability = 0.432
RMSEA index = 0.319 and the 90 % confidence intervals are 0.234 NA
BIC = -8.51
Fit based upon off diagonal values = 0.97Каждый объединяет хим элементы следующим образом:
Loadings:
MR1 MR2
depth -0.537 0.365
Li 0.993
Be 0.963
P -0.375 0.789
Sc 0.428 -0.650
Ti 0.983
V 0.367 0.256
Cr 0.890
Mn -0.181 0.827
Co 0.644 0.657
Ni 0.434 0.299
Cu 0.292 0.438
Zn 0.282 0.784
Rb 0.982
Sr 0.802 0.439
Y 0.974
Zr 0.805
Nb 0.988 -0.156
Mo 0.155 0.723
Ag -0.246 0.402
Cd
Sn 0.141 0.656
Sb 0.320 0.168
Cs 0.984 -0.136
Ba -0.164 0.781
La 0.945 0.182
Ce 0.854 0.417
Pr 0.937 0.194
Nd 0.937 0.172
Sm 0.943 0.101
Eu 0.932 0.151
Gd 0.957
Tb 0.975
Dy 0.961 -0.134
Ho 0.956 -0.147
Er 0.967 -0.151
Tm 0.977
Yb 0.991
Lu 0.984
Hf 0.904 -0.144
Ta 0.906
W 0.524 0.222
Tl 0.949 0.129
Pb 0.147 0.354
Bi 0.241 0.342
Th 0.993 -0.123
U 0.965
MR1 MR2
SS loadings 28.097 6.034
Proportion Var 0.598 0.128
Cumulative Var 0.598 0.7261 фактор описывает данные на 59.8%
1+2 факторы описывают данные на 72.6% 
2D репрезентация исходных наблюдений в новом пространстве факторов. 
3 factors
Проведём анализ с 3 факторами.
Factor Analysis using method = minres
Call: fa(r = lakes, nfactors = 3)
Warning: A Heywood case was detected.
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR3 MR2 h2 u2 com
depth -0.27 -0.32 0.69 0.687 0.3133 1.7
Li 0.94 0.07 -0.16 0.979 0.0214 1.1
Be 0.91 0.16 -0.02 0.950 0.0495 1.1
P -0.20 0.11 0.86 0.845 0.1554 1.1
Sc 0.37 -0.26 -0.57 0.554 0.4463 2.2
Ti 0.90 0.11 -0.21 0.966 0.0343 1.1
V 0.05 0.76 -0.24 0.622 0.3780 1.2
Cr 0.78 0.25 -0.13 0.824 0.1764 1.3
Mn 0.02 0.08 0.94 0.896 0.1038 1.0
Co 0.69 0.28 0.54 0.925 0.0749 2.3
Ni 0.10 0.83 -0.24 0.758 0.2421 1.2
Cu -0.03 0.89 -0.11 0.755 0.2449 1.0
Zn 0.08 0.84 0.32 0.916 0.0843 1.3
Rb 0.90 0.12 -0.18 0.962 0.0377 1.1
Sr 0.79 0.27 0.30 0.888 0.1123 1.5
Y 1.01 -0.08 0.03 0.980 0.0198 1.0
Zr 0.68 0.18 -0.26 0.677 0.3228 1.4
Nb 0.92 0.04 -0.22 0.977 0.0232 1.1
Mo -0.09 0.89 0.22 0.857 0.1433 1.1
Ag -0.04 -0.16 0.60 0.372 0.6279 1.2
Cd -0.08 0.24 -0.22 0.083 0.9175 2.2
Sn -0.06 0.77 0.22 0.654 0.3460 1.2
Sb 0.31 0.11 0.11 0.137 0.8632 1.5
Cs 0.91 0.07 -0.22 0.969 0.0311 1.1
Ba 0.04 0.05 0.90 0.814 0.1855 1.0
La 1.00 0.01 0.19 0.992 0.0078 1.1
Ce 0.88 0.20 0.33 0.971 0.0293 1.4
Pr 0.99 0.02 0.20 0.983 0.0172 1.1
Nd 0.99 -0.01 0.19 0.977 0.0233 1.1
Sm 1.01 -0.07 0.16 0.973 0.0275 1.1
Eu 1.01 -0.06 0.21 0.982 0.0182 1.1
Gd 1.02 -0.08 0.10 0.974 0.0259 1.0
Tb 1.00 -0.08 -0.02 0.968 0.0315 1.0
Dy 1.01 -0.17 -0.05 0.963 0.0366 1.1
Ho 1.01 -0.17 -0.06 0.956 0.0442 1.1
Er 1.01 -0.16 -0.07 0.970 0.0305 1.1
Tm 1.00 -0.09 -0.04 0.972 0.0278 1.0
Yb 1.01 -0.06 -0.05 0.992 0.0079 1.0
Lu 1.01 -0.08 -0.04 0.982 0.0176 1.0
Hf 0.80 0.12 -0.27 0.834 0.1659 1.3
Ta 0.77 0.32 -0.15 0.882 0.1175 1.4
W 0.30 0.55 -0.15 0.519 0.4814 1.7
Tl 0.87 0.22 -0.02 0.939 0.0609 1.1
Pb 0.21 0.08 0.34 0.168 0.8316 1.8
Bi 0.29 0.10 0.32 0.198 0.8019 2.2
Th 0.95 0.02 -0.17 0.981 0.0185 1.1
U 0.89 0.10 -0.17 0.928 0.0723 1.1
MR1 MR3 MR2
SS loadings 26.91 5.81 5.43
Proportion Var 0.57 0.12 0.12
Cumulative Var 0.57 0.70 0.81
Proportion Explained 0.71 0.15 0.14
Cumulative Proportion 0.71 0.86 1.00
With factor correlations of
MR1 MR3 MR2
MR1 1.00 0.32 -0.12
MR3 0.32 1.00 0.12
MR2 -0.12 0.12 1.00
Mean item complexity = 1.3
Test of the hypothesis that 3 factors are sufficient.
The degrees of freedom for the null model are 1081 and the objective function was 206.5 with Chi Square of 6917.69
The degrees of freedom for the model are 943 and the objective function was 99.67
The root mean square of the residuals (RMSR) is 0.06
The df corrected root mean square of the residuals is 0.07
The harmonic number of observations is 51 with the empirical chi square 427.3 with prob < 1
The total number of observations was 51 with Likelihood Chi Square = 3139.53 with prob < 1.6e-233
Tucker Lewis Index of factoring reliability = 0.536
RMSEA index = 0.293 and the 90 % confidence intervals are 0.208 NA
BIC = -568.18
Fit based upon off diagonal values = 0.99Каждый объединяет хим элементы следующим образом:
Loadings:
MR1 MR3 MR2
depth -0.266 -0.318 0.686
Li 0.935 -0.157
Be 0.911 0.160
P -0.198 0.105 0.862
Sc 0.374 -0.259 -0.566
Ti 0.897 0.114 -0.209
V 0.760 -0.243
Cr 0.779 0.248 -0.130
Mn 0.936
Co 0.690 0.284 0.545
Ni 0.100 0.826 -0.236
Cu 0.886 -0.107
Zn 0.842 0.316
Rb 0.902 0.122 -0.177
Sr 0.794 0.265 0.303
Y 1.015
Zr 0.683 0.182 -0.260
Nb 0.923 -0.224
Mo 0.892 0.224
Ag -0.163 0.598
Cd 0.240 -0.219
Sn 0.767 0.219
Sb 0.313 0.107 0.106
Cs 0.908 -0.224
Ba 0.897
La 0.997 0.193
Ce 0.877 0.196 0.329
Pr 0.989 0.200
Nd 0.995 0.192
Sm 1.014 0.156
Eu 1.014 0.209
Gd 1.018 0.100
Tb 1.003
Dy 1.014 -0.166
Ho 1.009 -0.174
Er 1.011 -0.161
Tm 1.004
Yb 1.006
Lu 1.007
Hf 0.802 0.120 -0.267
Ta 0.767 0.319 -0.148
W 0.305 0.553 -0.150
Tl 0.874 0.220
Pb 0.207 0.343
Bi 0.292 0.318
Th 0.952 -0.167
U 0.892 0.103 -0.174
MR1 MR3 MR2
SS loadings 26.451 5.397 5.340
Proportion Var 0.563 0.115 0.114
Cumulative Var 0.563 0.678 0.7911 фактор описывает данные на 56.3%
1+2 факторы описывают данные на 67.8%
1+2+3 факторы описывают данные на 79.1% 
3D репрезентация исходных наблюдений в новом пространстве факторов.
4 factors
Проведём анализ с 4 факторами.
Factor Analysis using method = minres
Call: fa(r = lakes, nfactors = 4)
Warning: A Heywood case was detected.
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR3 MR2 MR4 h2 u2 com
depth -0.20 -0.26 0.82 -0.25 0.86 0.1441 1.5
Li 0.95 0.08 -0.12 -0.07 0.98 0.0154 1.1
Be 0.90 0.15 -0.04 0.09 0.95 0.0486 1.1
P -0.18 0.14 0.90 -0.01 0.90 0.0953 1.1
Sc 0.41 -0.24 -0.49 -0.23 0.55 0.4459 2.9
Ti 0.92 0.13 -0.16 -0.10 0.98 0.0239 1.1
V 0.11 0.81 -0.12 -0.26 0.73 0.2657 1.3
Cr 0.78 0.25 -0.11 -0.01 0.82 0.1756 1.2
Mn 0.03 0.11 0.95 0.04 0.94 0.0623 1.0
Co 0.65 0.26 0.47 0.25 0.92 0.0763 2.5
Ni 0.15 0.87 -0.13 -0.22 0.85 0.1535 1.2
Cu -0.02 0.87 -0.08 0.02 0.75 0.2495 1.0
Zn 0.06 0.82 0.29 0.16 0.91 0.0913 1.3
Rb 0.93 0.14 -0.12 -0.11 0.98 0.0231 1.1
Sr 0.79 0.26 0.29 0.09 0.89 0.1118 1.5
Y 1.01 -0.08 0.02 0.03 0.98 0.0202 1.0
Zr 0.65 0.15 -0.31 0.13 0.70 0.3015 1.6
Nb 0.94 0.05 -0.19 -0.08 0.98 0.0193 1.1
Mo -0.09 0.88 0.24 0.07 0.86 0.1377 1.2
Ag -0.13 -0.24 0.42 0.48 0.52 0.4842 2.6
Cd -0.22 0.15 -0.49 0.62 0.52 0.4835 2.3
Sn -0.12 0.72 0.12 0.33 0.69 0.3090 1.5
Sb 0.14 -0.04 -0.23 0.88 0.81 0.1855 1.2
Cs 0.93 0.09 -0.18 -0.10 0.98 0.0238 1.1
Ba 0.05 0.08 0.91 0.04 0.85 0.1512 1.0
La 0.99 0.01 0.18 0.07 0.99 0.0087 1.1
Ce 0.88 0.20 0.33 0.05 0.98 0.0226 1.4
Pr 0.98 0.01 0.18 0.08 0.98 0.0186 1.1
Nd 0.98 -0.01 0.17 0.09 0.98 0.0247 1.1
Sm 1.00 -0.07 0.13 0.08 0.97 0.0287 1.1
Eu 1.00 -0.06 0.19 0.08 0.98 0.0199 1.1
Gd 1.00 -0.09 0.08 0.07 0.97 0.0266 1.0
Tb 1.01 -0.07 0.00 -0.02 0.97 0.0293 1.0
Dy 1.02 -0.16 -0.04 -0.02 0.96 0.0359 1.1
Ho 1.01 -0.17 -0.05 -0.02 0.96 0.0440 1.1
Er 1.02 -0.15 -0.05 -0.04 0.97 0.0289 1.1
Tm 1.00 -0.09 -0.04 0.01 0.97 0.0280 1.0
Yb 1.00 -0.06 -0.04 0.01 0.99 0.0080 1.0
Lu 1.00 -0.08 -0.05 0.02 0.98 0.0178 1.0
Hf 0.78 0.10 -0.29 0.07 0.84 0.1581 1.3
Ta 0.80 0.34 -0.08 -0.12 0.91 0.0926 1.4
W 0.25 0.50 -0.25 0.28 0.58 0.4248 2.7
Tl 0.85 0.20 -0.06 0.12 0.94 0.0568 1.2
Pb 0.06 -0.04 0.06 0.79 0.65 0.3511 1.0
Bi 0.15 -0.02 0.06 0.73 0.60 0.3957 1.1
Th 0.97 0.03 -0.13 -0.08 0.99 0.0124 1.1
U 0.89 0.10 -0.16 -0.01 0.93 0.0726 1.1
MR1 MR3 MR2 MR4
SS loadings 26.72 5.67 5.25 3.36
Proportion Var 0.57 0.12 0.11 0.07
Cumulative Var 0.57 0.69 0.80 0.87
Proportion Explained 0.65 0.14 0.13 0.08
Cumulative Proportion 0.65 0.79 0.92 1.00
With factor correlations of
MR1 MR3 MR2 MR4
MR1 1.00 0.31 -0.15 0.17
MR3 0.31 1.00 0.07 0.16
MR2 -0.15 0.07 1.00 0.16
MR4 0.17 0.16 0.16 1.00
Mean item complexity = 1.3
Test of the hypothesis that 4 factors are sufficient.
The degrees of freedom for the null model are 1081 and the objective function was 206.5 with Chi Square of 6917.69
The degrees of freedom for the model are 899 and the objective function was 93.36
The root mean square of the residuals (RMSR) is 0.03
The df corrected root mean square of the residuals is 0.03
The harmonic number of observations is 51 with the empirical chi square 104.99 with prob < 1
The total number of observations was 51 with Likelihood Chi Square = 2878.67 with prob < 1.7e-205
Tucker Lewis Index of factoring reliability = 0.55
RMSEA index = 0.29 and the 90 % confidence intervals are 0.201 NA
BIC = -656.04
Fit based upon off diagonal values = 1Каждый объединяет хим элементы следующим образом:
Loadings:
MR1 MR3 MR2 MR4
depth -0.199 -0.260 0.815 -0.255
Li 0.950 -0.121
Be 0.895 0.145
P -0.178 0.139 0.898
Sc 0.409 -0.238 -0.491 -0.225
Ti 0.919 0.126 -0.159 -0.104
V 0.111 0.814 -0.116 -0.264
Cr 0.783 0.246 -0.113
Mn 0.106 0.950
Co 0.652 0.261 0.471 0.250
Ni 0.150 0.868 -0.125 -0.215
Cu 0.873
Zn 0.820 0.288 0.165
Rb 0.926 0.138 -0.122 -0.112
Sr 0.785 0.262 0.290
Y 1.008
Zr 0.654 0.150 -0.308 0.133
Nb 0.938 -0.186
Mo 0.885 0.236
Ag -0.132 -0.235 0.423 0.485
Cd -0.223 0.146 -0.493 0.618
Sn -0.118 0.716 0.119 0.332
Sb 0.140 -0.230 0.876
Cs 0.927 -0.178
Ba 0.908
La 0.987 0.177
Ce 0.876 0.201 0.331
Pr 0.975 0.179
Nd 0.979 0.165
Sm 0.999 0.131
Eu 1.000 0.188
Gd 1.004
Tb 1.007
Dy 1.016 -0.160
Ho 1.009 -0.169
Er 1.016 -0.152
Tm 1.001
Yb 1.004
Lu 1.001
Hf 0.785 -0.292
Ta 0.796 0.338 -0.121
W 0.252 0.502 -0.246 0.277
Tl 0.852 0.199 0.124
Pb 0.789
Bi 0.153 0.732
Th 0.967 -0.129
U 0.894 0.101 -0.162
MR1 MR3 MR2 MR4
SS loadings 26.198 5.269 5.115 3.224
Proportion Var 0.557 0.112 0.109 0.069
Cumulative Var 0.557 0.670 0.778 0.8471 фактор описывает данные на 55.7%
1+2 факторы описывают данные на 67%
1+2+3 факторы описывают данные на 77.8%
1+2+3+4 факторы описывают данные на 84.7% 
Визуальную репрезентацию в размерности 4 не смогла осуществить.